메뉴 건너뛰기




Volumn 38, Issue 12, 2006, Pages 868-898

Oblique interactions of weakly nonlinear long waves in dispersive systems

Author keywords

Kadomtsev Petviashvili equation; Mach reflection; Nonlinear wave propagation; Oblique interaction; Solitary waves; Soliton; Soliton resonance

Indexed keywords

MATHEMATICAL MODELS; MECHANICAL WAVES; WAVE EQUATIONS; WAVEFORM ANALYSIS;

EID: 33750323501     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fluiddyn.2006.07.002     Document Type: Article
Times cited : (22)

References (116)
  • 2
    • 36749108920 scopus 로고
    • Solitons and rational solutions of nonlinear evolution equations
    • Ablowitz M.J., and Satsuma J. Solitons and rational solutions of nonlinear evolution equations. J. Math. Phys. 19 (1978) 2180-2186
    • (1978) J. Math. Phys. , vol.19 , pp. 2180-2186
    • Ablowitz, M.J.1    Satsuma, J.2
  • 3
    • 0000085266 scopus 로고
    • Long internal waves in fluids of great depth
    • Ablowitz M.J., and Segur H. Long internal waves in fluids of great depth. Stud. Appl. Math. 62 (1980) 249-262
    • (1980) Stud. Appl. Math. , vol.62 , pp. 249-262
    • Ablowitz, M.J.1    Segur, H.2
  • 5
    • 0034642817 scopus 로고    scopus 로고
    • A novel class of solutions of the non-stationary Schrödinger and Kadomtsev-Petviashvili I equations
    • Ablowitz M.J., Chakravarty S., Trubatch A.D., and Villarroel J. A novel class of solutions of the non-stationary Schrödinger and Kadomtsev-Petviashvili I equations. Phys. Lett. A 267 (2000) 132-146
    • (2000) Phys. Lett. A , vol.267 , pp. 132-146
    • Ablowitz, M.J.1    Chakravarty, S.2    Trubatch, A.D.3    Villarroel, J.4
  • 6
    • 0021976247 scopus 로고
    • Two-dimensional multisolitons: stationary solutions of Kadomtsev-Petviashvili equation
    • Abramyan L.A., and Stepanyants Yu.A. Two-dimensional multisolitons: stationary solutions of Kadomtsev-Petviashvili equation. Radiophys. Quantum Electron. 28 (1985) 20-26
    • (1985) Radiophys. Quantum Electron. , vol.28 , pp. 20-26
    • Abramyan, L.A.1    Stepanyants, Yu.A.2
  • 7
    • 0002411595 scopus 로고
    • Three-dimensional long water-wave phenomena
    • Akylas T.R. Three-dimensional long water-wave phenomena. Annu. Rev. Fluid Mech. 26 (1994) 191-210
    • (1994) Annu. Rev. Fluid Mech. , vol.26 , pp. 191-210
    • Akylas, T.R.1
  • 8
    • 0010538309 scopus 로고
    • Interpretation of three-soliton interactions in terms of resonant triads
    • Anker D., and Freeman N.C. Interpretation of three-soliton interactions in terms of resonant triads. J. Fluid Mech. 87 (1978) 17-31
    • (1978) J. Fluid Mech. , vol.87 , pp. 17-31
    • Anker, D.1    Freeman, N.C.2
  • 9
    • 84902775564 scopus 로고
    • Internal waves of permanent form in fluids of great depth
    • Benjamin T.B. Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29 (1967) 559-592
    • (1967) J. Fluid Mech. , vol.29 , pp. 559-592
    • Benjamin, T.B.1
  • 10
    • 85163152910 scopus 로고
    • On the interactions of permanent waves of finite amplitude
    • Benney D.J., and Luke J.C. On the interactions of permanent waves of finite amplitude. J. Math. and Phys. 43 (1964) 309-313
    • (1964) J. Math. and Phys. , vol.43 , pp. 309-313
    • Benney, D.J.1    Luke, J.C.2
  • 11
    • 0032279659 scopus 로고    scopus 로고
    • Solitons and electromagnetic wave propagation through cold collision free plasma
    • Bindu S.G., and Kuriakose V.C. Solitons and electromagnetic wave propagation through cold collision free plasma. J. Phys. Soc. Japan 67 (1998) 4031-4036
    • (1998) J. Phys. Soc. Japan , vol.67 , pp. 4031-4036
    • Bindu, S.G.1    Kuriakose, V.C.2
  • 12
    • 33645666408 scopus 로고    scopus 로고
    • Soliton solutions of the Kadomtsev-Petviashvili II equation
    • Biondini G., and Chakravarty S. Soliton solutions of the Kadomtsev-Petviashvili II equation. J. Math. Phys. 47 (2006) 033514
    • (2006) J. Math. Phys. , vol.47 , pp. 033514
    • Biondini, G.1    Chakravarty, S.2
  • 13
    • 0242350970 scopus 로고    scopus 로고
    • On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy
    • Biondini G., and Kodama Y. On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy. J. Phys. A 36 (2003) 10519-10536
    • (2003) J. Phys. A , vol.36 , pp. 10519-10536
    • Biondini, G.1    Kodama, Y.2
  • 15
    • 0037553631 scopus 로고
    • "The wave" "par excellence", the solitary progressive great wave of equilibrium of the fluid: an early history of the solitary wave
    • Lakshmanan M. (Ed), Springer, Berlin
    • Bullough R.K. "The wave" "par excellence", the solitary progressive great wave of equilibrium of the fluid: an early history of the solitary wave. In: Lakshmanan M. (Ed). Solitons-Introduction and Applications (1988), Springer, Berlin 7-42
    • (1988) Solitons-Introduction and Applications , pp. 7-42
    • Bullough, R.K.1
  • 16
    • 51249182682 scopus 로고
    • Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation
    • Calogero F., and Degasperis A. Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation. Lett. Nuovo Cimento 23 (1978) 150-154
    • (1978) Lett. Nuovo Cimento , vol.23 , pp. 150-154
    • Calogero, F.1    Degasperis, A.2
  • 17
    • 33750335921 scopus 로고
    • Observation of diverging cylindrical solitons excited with a probe
    • Chen T., and Schott L. Observation of diverging cylindrical solitons excited with a probe. Phys. Lett. A 58 (1976) 459-461
    • (1976) Phys. Lett. A , vol.58 , pp. 459-461
    • Chen, T.1    Schott, L.2
  • 18
    • 33750298406 scopus 로고
    • Diverging solitons and their transition to dispersive waves
    • Chen T., and Schott L. Diverging solitons and their transition to dispersive waves. Plasma Phys. 19 (1977) 959-967
    • (1977) Plasma Phys. , vol.19 , pp. 959-967
    • Chen, T.1    Schott, L.2
  • 19
    • 21344487622 scopus 로고
    • Lattice solitons directly by the bilinear method
    • Chow K.W. Lattice solitons directly by the bilinear method. J. Math. Phys. 35 (1994) 4057-4066
    • (1994) J. Math. Phys. , vol.35 , pp. 4057-4066
    • Chow, K.W.1
  • 20
    • 2842543348 scopus 로고
    • Spike solution for radially symmetric solitary waves
    • Cumberbatch E. Spike solution for radially symmetric solitary waves. Phys. Fluids 21 (1978) 374-376
    • (1978) Phys. Fluids , vol.21 , pp. 374-376
    • Cumberbatch, E.1
  • 21
    • 0039322894 scopus 로고
    • An analytical solution of the axial symmetric KdV equation
    • (in Russian)
    • Dryuma V.S. An analytical solution of the axial symmetric KdV equation. Izv. Akad. Nauk Mold. SSSR 3 (1976) 87-89 (in Russian)
    • (1976) Izv. Akad. Nauk Mold. SSSR , vol.3 , pp. 87-89
    • Dryuma, V.S.1
  • 22
    • 84928007477 scopus 로고
    • Theta functions and non-linear equations
    • Dubrovin B.A. Theta functions and non-linear equations. Russ. Math. Surv. 36 (1981) 11-92
    • (1981) Russ. Math. Surv. , vol.36 , pp. 11-92
    • Dubrovin, B.A.1
  • 23
    • 0001740722 scopus 로고
    • Two-dimensional interaction of ion-acoustic solitons
    • Folkes P.A., Ikezi H., and Davis R. Two-dimensional interaction of ion-acoustic solitons. Phys. Rev. Lett. 45 (1980) 902-904
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 902-904
    • Folkes, P.A.1    Ikezi, H.2    Davis, R.3
  • 24
    • 0019241426 scopus 로고
    • Soliton interactions in two dimensions
    • Freeman N.C. Soliton interactions in two dimensions. Adv. Appl. Mech. 20 (1980) 1-37
    • (1980) Adv. Appl. Mech. , vol.20 , pp. 1-37
    • Freeman, N.C.1
  • 25
    • 0006740209 scopus 로고
    • Reflection of obliquely incident solitary waves
    • Funakoshi M. Reflection of obliquely incident solitary waves. J. Phys. Soc. Japan 49 (1980) 2371-2379
    • (1980) J. Phys. Soc. Japan , vol.49 , pp. 2371-2379
    • Funakoshi, M.1
  • 26
    • 0019584517 scopus 로고
    • On the time evolution of a solitary wave reflected by an oblique wall
    • Funakoshi M. On the time evolution of a solitary wave reflected by an oblique wall. Rep. Res. Inst. Appl. Mech. Kyushu Univ. 29 (1981) 79-93
    • (1981) Rep. Res. Inst. Appl. Mech. Kyushu Univ. , vol.29 , pp. 79-93
    • Funakoshi, M.1
  • 27
    • 4243603399 scopus 로고
    • On the oblique collision of unequal amplitude ion-acoustic solitons in a field-free plasma
    • Gabl E.F., and Lonngren K.E. On the oblique collision of unequal amplitude ion-acoustic solitons in a field-free plasma. Phys. Lett. A 100 (1984) 153-155
    • (1984) Phys. Lett. A , vol.100 , pp. 153-155
    • Gabl, E.F.1    Lonngren, K.E.2
  • 29
    • 84980193643 scopus 로고
    • Korteweg-de Vries equation and generalizations. VI. Methods for exact solution
    • Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Korteweg-de Vries equation and generalizations. VI. Methods for exact solution. Commun. Pure Appl. Math. 27 (1974) 97-133
    • (1974) Commun. Pure Appl. Math. , vol.27 , pp. 97-133
    • Gardner, C.S.1    Greene, J.M.2    Kruskal, M.D.3    Miura, R.M.4
  • 30
    • 0024877769 scopus 로고
    • Two-dimensional periodic waves in shallow water
    • Hammack J., Scheffner N., and Segur H. Two-dimensional periodic waves in shallow water. J. Fluid Mech. 209 (1989) 567-589
    • (1989) J. Fluid Mech. , vol.209 , pp. 567-589
    • Hammack, J.1    Scheffner, N.2    Segur, H.3
  • 31
    • 0028976320 scopus 로고
    • Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves
    • Hammack J., McCallister D., Scheffner N., and Segur H. Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves. J. Fluid Mech. 285 (1995) 95-122
    • (1995) J. Fluid Mech. , vol.285 , pp. 95-122
    • Hammack, J.1    McCallister, D.2    Scheffner, N.3    Segur, H.4
  • 32
    • 0039042658 scopus 로고
    • Observations of ion-acoustic cylindrical solitons
    • Hershkowitz N., and Romesser T. Observations of ion-acoustic cylindrical solitons. Phys. Rev. Lett. 32 (1974) 581-583
    • (1974) Phys. Rev. Lett. , vol.32 , pp. 581-583
    • Hershkowitz, N.1    Romesser, T.2
  • 34
    • 33750298482 scopus 로고    scopus 로고
    • Infeld, E., Rowlands, G., 1990. Nonlinear Waves, Solitons and Chaos. Cambridge University Press, Cambridge (second ed., 2000).
  • 35
    • 0041381049 scopus 로고    scopus 로고
    • On various solutions of the coupled KP equation
    • Isojima S., Willox R., and Satsuma J. On various solutions of the coupled KP equation. J. Phys. A 35 (2002) 6893-6909
    • (2002) J. Phys. A , vol.35 , pp. 6893-6909
    • Isojima, S.1    Willox, R.2    Satsuma, J.3
  • 36
    • 0004531797 scopus 로고
    • On the inverse scattering transform, the cylindrical Korteweg-de Vries equation and similarity solutions
    • Johnson R.S. On the inverse scattering transform, the cylindrical Korteweg-de Vries equation and similarity solutions. Phys. Lett. A 72 (1979) 197-199
    • (1979) Phys. Lett. A , vol.72 , pp. 197-199
    • Johnson, R.S.1
  • 37
    • 0001469929 scopus 로고
    • Water waves and Korteweg-de Vries equations
    • Johnson R.S. Water waves and Korteweg-de Vries equations. J. Fluid Mech. 97 (1980) 701-719
    • (1980) J. Fluid Mech. , vol.97 , pp. 701-719
    • Johnson, R.S.1
  • 38
    • 84971946808 scopus 로고
    • On the oblique interaction of a large and a small solitary wave
    • Johnson R.S. On the oblique interaction of a large and a small solitary wave. J. Fluid Mech. 120 (1982) 49-70
    • (1982) J. Fluid Mech. , vol.120 , pp. 49-70
    • Johnson, R.S.1
  • 39
    • 0002097462 scopus 로고    scopus 로고
    • A note on an asymptotic solution of the cylindrical Korteweg-de Vries equation
    • Johnson R.S. A note on an asymptotic solution of the cylindrical Korteweg-de Vries equation. Wave Motion 30 (1999) 1-16
    • (1999) Wave Motion , vol.30 , pp. 1-16
    • Johnson, R.S.1
  • 40
    • 0001204563 scopus 로고
    • A solution of the inverse scattering problem for the Kadomtsev-Petviashvili equation by the method of separation of variables
    • Johnson R.S., and Thompson S. A solution of the inverse scattering problem for the Kadomtsev-Petviashvili equation by the method of separation of variables. Phys. Lett. A 66 (1978) 279-281
    • (1978) Phys. Lett. A , vol.66 , pp. 279-281
    • Johnson, R.S.1    Thompson, S.2
  • 41
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersing media
    • Kadomtsev B.B., and Petviashvili V.I. On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15 (1970) 539-541
    • (1970) Sov. Phys. Dokl. , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 42
    • 0019081616 scopus 로고
    • Interaction of ion-acoustic solitons in two-dimensional space
    • Kako F., and Yajima N. Interaction of ion-acoustic solitons in two-dimensional space. J. Phys. Soc. Japan 49 (1980) 2063-2071
    • (1980) J. Phys. Soc. Japan , vol.49 , pp. 2063-2071
    • Kako, F.1    Yajima, N.2
  • 43
    • 0003133444 scopus 로고
    • Interaction of ion-acoustic solitons in multi-dimensional space. II
    • Kako F., and Yajima N. Interaction of ion-acoustic solitons in multi-dimensional space. II. J. Phys. Soc. Japan 51 (1982) 311-322
    • (1982) J. Phys. Soc. Japan , vol.51 , pp. 311-322
    • Kako, F.1    Yajima, N.2
  • 44
    • 0017998674 scopus 로고
    • Solitary waves on a two-layer fluid
    • Kakutani T., and Yamasaki N. Solitary waves on a two-layer fluid. J. Phys. Soc. Japan 45 (1978) 674-679
    • (1978) J. Phys. Soc. Japan , vol.45 , pp. 674-679
    • Kakutani, T.1    Yamasaki, N.2
  • 45
    • 5344237509 scopus 로고
    • Nonlinear resonances and colliding spherical ion-acoustic solitons
    • Kaup D.J. Nonlinear resonances and colliding spherical ion-acoustic solitons. Physica D 2 (1981) 389-394
    • (1981) Physica D , vol.2 , pp. 389-394
    • Kaup, D.J.1
  • 46
    • 3042781172 scopus 로고    scopus 로고
    • Physical mechanisms of the rogue wave phenomenon
    • Kharif C., and Pelinovsky E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids 22 (2003) 603-634
    • (2003) Eur. J. Mech. B/Fluids , vol.22 , pp. 603-634
    • Kharif, C.1    Pelinovsky, E.2
  • 47
    • 0347337917 scopus 로고
    • Cylindrical and spherical Korteweg-de Vries solitary waves
    • Ko K., and Kuehl H.H. Cylindrical and spherical Korteweg-de Vries solitary waves. Phys. Fluids 22 (1979) 1343-1348
    • (1979) Phys. Fluids , vol.22 , pp. 1343-1348
    • Ko, K.1    Kuehl, H.H.2
  • 48
    • 9944220897 scopus 로고    scopus 로고
    • Young diagrams and N-soliton solutions of the KP equation
    • Kodama Y. Young diagrams and N-soliton solutions of the KP equation. J. Phys. A 37 (2004) 11169-11190
    • (2004) J. Phys. A , vol.37 , pp. 11169-11190
    • Kodama, Y.1
  • 50
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • Korteweg D.J., and de Vries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. Mag. Ser. 5 39 (1895) 422-443
    • (1895) Philos. Mag. Ser. 5 , vol.39 , pp. 422-443
    • Korteweg, D.J.1    de Vries, G.2
  • 51
    • 0009419966 scopus 로고
    • An algebraic geometry construction of the Zakharov-Shabat equations and their periodic solutions
    • Krichever I.M. An algebraic geometry construction of the Zakharov-Shabat equations and their periodic solutions. Sov. Math. Dokl. 17 (1976) 394-397
    • (1976) Sov. Math. Dokl. , vol.17 , pp. 394-397
    • Krichever, I.M.1
  • 52
    • 0010989303 scopus 로고
    • Methods of algebraic geometry in the theory of non-linear equations
    • Krichever I.M. Methods of algebraic geometry in the theory of non-linear equations. Russ. Math. Surv. 32 (1977) 185-213
    • (1977) Russ. Math. Surv. , vol.32 , pp. 185-213
    • Krichever, I.M.1
  • 53
    • 84937890094 scopus 로고
    • Spectral theory of two-dimensional periodic operators and its applications
    • Krichever I.M. Spectral theory of two-dimensional periodic operators and its applications. Russ. Math. Surv. 44 (1989) 145-225
    • (1989) Russ. Math. Surv. , vol.44 , pp. 145-225
    • Krichever, I.M.1
  • 54
    • 0000585502 scopus 로고
    • Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction
    • Manakov S.V., Zakharov V.E., Bordag L.A., Its A.R., and Matveev V.B. Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction. Phys. Lett. A 63 (1977) 205-206
    • (1977) Phys. Lett. A , vol.63 , pp. 205-206
    • Manakov, S.V.1    Zakharov, V.E.2    Bordag, L.A.3    Its, A.R.4    Matveev, V.B.5
  • 55
    • 33750357311 scopus 로고    scopus 로고
    • Maruno, K., Tsuji, H., Oikawa, M., 2006. A possible mechanism of generation of extreme waves in shallow water, in preparation.
  • 56
    • 0037786131 scopus 로고
    • Exact multi-soliton solution of the Benjamin-Ono equation
    • Matsuno Y. Exact multi-soliton solution of the Benjamin-Ono equation. J. Phys. A 12 (1979) 619-621
    • (1979) J. Phys. A , vol.12 , pp. 619-621
    • Matsuno, Y.1
  • 58
    • 33746669963 scopus 로고    scopus 로고
    • Oblique interaction of interfacial solitary waves in a two-layer deep fluid
    • Matsuno Y. Oblique interaction of interfacial solitary waves in a two-layer deep fluid. Proc. Roy. Soc. London A 454 (1998) 835-856
    • (1998) Proc. Roy. Soc. London A , vol.454 , pp. 835-856
    • Matsuno, Y.1
  • 59
    • 0016093836 scopus 로고
    • Cylindrical solitons
    • Maxon S., and Viecelli J. Cylindrical solitons. Phys. Fluids 17 (1974) 1614-1616
    • (1974) Phys. Fluids , vol.17 , pp. 1614-1616
    • Maxon, S.1    Viecelli, J.2
  • 61
    • 0018925569 scopus 로고
    • On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions
    • Maxworthy T. On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions. J. Fluid Mech. 96 (1980) 47-64
    • (1980) J. Fluid Mech. , vol.96 , pp. 47-64
    • Maxworthy, T.1
  • 62
    • 84958437409 scopus 로고
    • On the Mach reflexion of a solitary wave
    • Melville W.K. On the Mach reflexion of a solitary wave. J. Fluid Mech. 98 (1980) 285-297
    • (1980) J. Fluid Mech. , vol.98 , pp. 285-297
    • Melville, W.K.1
  • 63
    • 0016903592 scopus 로고
    • Obliquely interacting solitary waves
    • Miles J.M. Obliquely interacting solitary waves. J. Fluid Mech. 79 (1977) 157-169
    • (1977) J. Fluid Mech. , vol.79 , pp. 157-169
    • Miles, J.M.1
  • 64
    • 0016908018 scopus 로고
    • Resonantly interacting solitary waves
    • Miles J.M. Resonantly interacting solitary waves. J. Fluid Mech. 79 (1977) 171-179
    • (1977) J. Fluid Mech. , vol.79 , pp. 171-179
    • Miles, J.M.1
  • 65
    • 0013723737 scopus 로고
    • An axisymmetric Boussinesq wave
    • Miles J.M. An axisymmetric Boussinesq wave. J. Fluid Mech. 84 (1978) 181-191
    • (1978) J. Fluid Mech. , vol.84 , pp. 181-191
    • Miles, J.M.1
  • 66
    • 0000905823 scopus 로고
    • On internal solitary waves
    • Miles J.M. On internal solitary waves. Tellus 31 (1979) 456-462
    • (1979) Tellus , vol.31 , pp. 456-462
    • Miles, J.M.1
  • 67
    • 0019559935 scopus 로고
    • The Korteweg-de Vries equation: a historical essay
    • Miles J.M. The Korteweg-de Vries equation: a historical essay. J. Fluid Mech. 106 (1981) 131-147
    • (1981) J. Fluid Mech. , vol.106 , pp. 131-147
    • Miles, J.M.1
  • 68
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: a survey of results
    • Miura R.M. The Korteweg-de Vries equation: a survey of results. SIAM Rev. 18 (1976) 412-459
    • (1976) SIAM Rev. , vol.18 , pp. 412-459
    • Miura, R.M.1
  • 69
    • 0346912618 scopus 로고
    • Interactions between two y-periodic solitons: solutions to the Kadomtsev-Petviashvili equation with positive dispersion
    • Murakami Y., and Tajiri M. Interactions between two y-periodic solitons: solutions to the Kadomtsev-Petviashvili equation with positive dispersion. Wave Motion 14 (1991) 169-185
    • (1991) Wave Motion , vol.14 , pp. 169-185
    • Murakami, Y.1    Tajiri, M.2
  • 70
    • 33845683273 scopus 로고
    • Resonant interaction between line soliton and Y-periodic soliton: solutions to the Kadomtsev-Petviashvili equation with positive dispersion
    • Murakami Y., and Tajiri M. Resonant interaction between line soliton and Y-periodic soliton: solutions to the Kadomtsev-Petviashvili equation with positive dispersion. J. Phys. Soc. Japan 61 (1992) 791-805
    • (1992) J. Phys. Soc. Japan , vol.61 , pp. 791-805
    • Murakami, Y.1    Tajiri, M.2
  • 71
    • 0000469268 scopus 로고
    • Bäcklund transformation of the cylindrical KdV equation
    • Nakamura A. Bäcklund transformation of the cylindrical KdV equation. J. Phys. Soc. Japan 49 (1980) 2380-2386
    • (1980) J. Phys. Soc. Japan , vol.49 , pp. 2380-2386
    • Nakamura, A.1
  • 72
    • 0000588008 scopus 로고
    • Soliton solutions of the cylindrical KdV equation
    • Nakamura A., and Chen H.H. Soliton solutions of the cylindrical KdV equation. J. Phys. Soc. Japan 50 (1981) 711-718
    • (1981) J. Phys. Soc. Japan , vol.50 , pp. 711-718
    • Nakamura, A.1    Chen, H.H.2
  • 73
    • 0000388788 scopus 로고    scopus 로고
    • Oblique collision of modified Korteweg-de Vries ion-acoustic solitons
    • Nakamura Y., Bailung H., and Lonngren K.E. Oblique collision of modified Korteweg-de Vries ion-acoustic solitons. Phys. Plasmas 6 (1999) 3466-3470
    • (1999) Phys. Plasmas , vol.6 , pp. 3466-3470
    • Nakamura, Y.1    Bailung, H.2    Lonngren, K.E.3
  • 74
    • 4243670535 scopus 로고
    • Breakdown of Zakharov-Shabat theory and soliton creation
    • Newell A.C., and Redekopp L.G. Breakdown of Zakharov-Shabat theory and soliton creation. Phys. Rev. Lett. 38 (1977) 377-380
    • (1977) Phys. Rev. Lett. , vol.38 , pp. 377-380
    • Newell, A.C.1    Redekopp, L.G.2
  • 75
    • 0012755260 scopus 로고
    • Oblique collision of plane ion-acoustic solitons
    • Nishida Y., and Nagasawa T. Oblique collision of plane ion-acoustic solitons. Phys. Rev. Lett. 45 (1980) 1626-1629
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 1626-1629
    • Nishida, Y.1    Nagasawa, T.2
  • 76
    • 33750354629 scopus 로고
    • Experimental verification of the characteristics of ion-acoustic cylindrical solitons
    • Nishida Y., Nagasawa T., and Kawamoto S. Experimental verification of the characteristics of ion-acoustic cylindrical solitons. Phys. Lett. A 69 (1978) 196-198
    • (1978) Phys. Lett. A , vol.69 , pp. 196-198
    • Nishida, Y.1    Nagasawa, T.2    Kawamoto, S.3
  • 77
    • 56249149020 scopus 로고
    • The Kadomtsev-Petviashvili equation: the trace method and the soliton resonances
    • Ohkuma K., and Wadati M. The Kadomtsev-Petviashvili equation: the trace method and the soliton resonances. J. Phys. Soc. Japan 52 (1983) 749-760
    • (1983) J. Phys. Soc. Japan , vol.52 , pp. 749-760
    • Ohkuma, K.1    Wadati, M.2
  • 78
    • 33750314269 scopus 로고    scopus 로고
    • Ohta, Y., Satsuma, J., Takahashi, D., Tokihiro, T., 1988. An elementary introduction to Sato theory. Progr. Theor. Phys. (Suppl. 94), 210-241.
  • 79
    • 0000867411 scopus 로고
    • On the weak interactions of the Benjamin-Ono solitons
    • (in Japanese)
    • Oikawa M. On the weak interactions of the Benjamin-Ono solitons. Bull. Res. Inst. Appl. Mech. Kyushu Univ. 60 (1984) 467-472 (in Japanese)
    • (1984) Bull. Res. Inst. Appl. Mech. Kyushu Univ. , vol.60 , pp. 467-472
    • Oikawa, M.1
  • 80
    • 0006744418 scopus 로고
    • Interactions of solitary waves-a perturbation approach to nonlinear systems-
    • Oikawa M., and Yajima N. Interactions of solitary waves-a perturbation approach to nonlinear systems-. J. Phys. Soc. Japan 34 (1973) 1093-1099
    • (1973) J. Phys. Soc. Japan , vol.34 , pp. 1093-1099
    • Oikawa, M.1    Yajima, N.2
  • 81
    • 0016459710 scopus 로고
    • Algebraic solitary waves in stratified fluids
    • Ono H. Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39 (1975) 1082-1091
    • (1975) J. Phys. Soc. Japan , vol.39 , pp. 1082-1091
    • Ono, H.1
  • 82
    • 23044454956 scopus 로고    scopus 로고
    • Degenerate four-virtual-soliton resonance for the KP-II
    • Pashaev O.K., and Francisco M.L.Y. Degenerate four-virtual-soliton resonance for the KP-II. Theor. Math. Phys. 144 (2005) 1022-1029
    • (2005) Theor. Math. Phys. , vol.144 , pp. 1022-1029
    • Pashaev, O.K.1    Francisco, M.L.Y.2
  • 83
    • 0001715553 scopus 로고
    • A modified Korteweg-de Vries equation in electrohydrodynamics
    • Perelman T.L., Fridman A.Kh., and El'yashevich M.M. A modified Korteweg-de Vries equation in electrohydrodynamics. Sov. Phys. JETP. 39 (1974) 643-646
    • (1974) Sov. Phys. JETP. , vol.39 , pp. 643-646
    • Perelman, T.L.1    Fridman, A.Kh.2    El'yashevich, M.M.3
  • 84
    • 0012607211 scopus 로고
    • On the relationship between the N-soliton solution of the modified Korteweg-de Vries equation and the KdV equation solution
    • Perelman T.L., Fridman A.Kh., and El'yashevich M.M. On the relationship between the N-soliton solution of the modified Korteweg-de Vries equation and the KdV equation solution. Phys. Lett. A 47 (1974) 321-323
    • (1974) Phys. Lett. A , vol.47 , pp. 321-323
    • Perelman, T.L.1    Fridman, A.Kh.2    El'yashevich, M.M.3
  • 85
    • 33750361052 scopus 로고    scopus 로고
    • Perroud, P.H., 1957. The solitary wave reflection along a straight vertical wall at oblique incidence. Ph.D. Thesis, University of California, Berkeley.
  • 86
    • 0001341517 scopus 로고    scopus 로고
    • A direct and inverse problem for wave crests modelled by interactions of two solitons
    • Peterson P., and van Groesen E. A direct and inverse problem for wave crests modelled by interactions of two solitons. Physica D 141 (2000) 316-332
    • (2000) Physica D , vol.141 , pp. 316-332
    • Peterson, P.1    van Groesen, E.2
  • 88
    • 0001841091 scopus 로고
    • Soliton equations as dynamical systems on a infinite dimensional Grassmann manifolds
    • Sato M. Soliton equations as dynamical systems on a infinite dimensional Grassmann manifolds. RIAM Kokyuroku Kyoto Univ. 439 (1981) 30-46
    • (1981) RIAM Kokyuroku Kyoto Univ. , vol.439 , pp. 30-46
    • Sato, M.1
  • 89
    • 0001619573 scopus 로고
    • N-soliton solution of the two-dimensional Korteweg-de Vries equation
    • Satsuma J. N-soliton solution of the two-dimensional Korteweg-de Vries equation. J. Phys. Soc. Japan 40 (1976) 286-290
    • (1976) J. Phys. Soc. Japan , vol.40 , pp. 286-290
    • Satsuma, J.1
  • 90
    • 0022199495 scopus 로고
    • An analytical model of periodic waves in shallow water
    • Segur H., and Finkel A. An analytical model of periodic waves in shallow water. Stud. Appl. Math. 73 (1985) 183-220
    • (1985) Stud. Appl. Math. , vol.73 , pp. 183-220
    • Segur, H.1    Finkel, A.2
  • 91
    • 14244268920 scopus 로고    scopus 로고
    • Interaction of Kadomtsev-Petviashvili solitons with unequal amplitudes
    • Soomere T. Interaction of Kadomtsev-Petviashvili solitons with unequal amplitudes. Phys. Lett. A 332 (2004) 74-81
    • (2004) Phys. Lett. A , vol.332 , pp. 74-81
    • Soomere, T.1
  • 92
    • 7544227818 scopus 로고    scopus 로고
    • Extreme elevations and slopes of interacting solitons in shallow water
    • Soomere T., and Engelbrecht J. Extreme elevations and slopes of interacting solitons in shallow water. Wave Motion 41 (2005) 179-192
    • (2005) Wave Motion , vol.41 , pp. 179-192
    • Soomere, T.1    Engelbrecht, J.2
  • 93
    • 0019624864 scopus 로고
    • Experimental investigation of cylindrically diverging solitons in an electric lattice
    • Stepanyants Yu.A. Experimental investigation of cylindrically diverging solitons in an electric lattice. Wave Motion 3 (1981) 335-341
    • (1981) Wave Motion , vol.3 , pp. 335-341
    • Stepanyants, Yu.A.1
  • 94
    • 36849102307 scopus 로고
    • Korteweg-de Vries equation and generalizations. III. Derivation of the Korteweg-de Vries equation and Burgers equation
    • Su C.H., and Gardner C.S. Korteweg-de Vries equation and generalizations. III. Derivation of the Korteweg-de Vries equation and Burgers equation. J. Math. Phys. 10 (1969) 536-539
    • (1969) J. Math. Phys. , vol.10 , pp. 536-539
    • Su, C.H.1    Gardner, C.S.2
  • 95
    • 0039575938 scopus 로고
    • Two-dimensional multisoliton solutions: periodic soliton solutions to the Kadomtsev-Petviashvili equation with positive dispersion
    • Tajiri M., and Murakami Y. Two-dimensional multisoliton solutions: periodic soliton solutions to the Kadomtsev-Petviashvili equation with positive dispersion. J. Phys. Soc. Japan 58 (1989) 3029-3032
    • (1989) J. Phys. Soc. Japan , vol.58 , pp. 3029-3032
    • Tajiri, M.1    Murakami, Y.2
  • 96
    • 0000385259 scopus 로고
    • The periodic soliton resonance: solutions to the Kadomtsev-Petviashvili equation with positive dispersion
    • Tajiri M., and Murakami Y. The periodic soliton resonance: solutions to the Kadomtsev-Petviashvili equation with positive dispersion. Phys. Lett. A 143 (1990) 217-220
    • (1990) Phys. Lett. A , vol.143 , pp. 217-220
    • Tajiri, M.1    Murakami, Y.2
  • 97
    • 21144482481 scopus 로고
    • Lattice soliton: solutions to the Kadomtsev-Petviashvili equation with positive dispersion
    • Tajiri M., and Murakami Y. Lattice soliton: solutions to the Kadomtsev-Petviashvili equation with positive dispersion. J. Math. Phys. 34 (1993) 2400-2411
    • (1993) J. Math. Phys. , vol.34 , pp. 2400-2411
    • Tajiri, M.1    Murakami, Y.2
  • 98
    • 0027392259 scopus 로고
    • Mach reflection of a large-amplitude solitary wave
    • Tanaka M. Mach reflection of a large-amplitude solitary wave. J. Fluid Mech. 248 (1993) 637-661
    • (1993) J. Fluid Mech. , vol.248 , pp. 637-661
    • Tanaka, M.1
  • 99
    • 77952528320 scopus 로고
    • Reductive perturbation method in nonlinear wave propagation
    • Taniuti T., and Wei C.C. Reductive perturbation method in nonlinear wave propagation. I. J. Phys. Soc. Japan 24 (1968) 941-946
    • (1968) I. J. Phys. Soc. Japan , vol.24 , pp. 941-946
    • Taniuti, T.1    Wei, C.C.2
  • 100
    • 33750302168 scopus 로고    scopus 로고
    • Occurrence of extreme or freak ocean waves (a current research in marine hydrodynamics)
    • (in Japanese)
    • Tomita H., Waseda T., Kawamura T., and Rheem C.-K. Occurrence of extreme or freak ocean waves (a current research in marine hydrodynamics). Nagare 25 (2006) 39-48 (in Japanese)
    • (2006) Nagare , vol.25 , pp. 39-48
    • Tomita, H.1    Waseda, T.2    Kawamura, T.3    Rheem, C.-K.4
  • 101
    • 21344494647 scopus 로고
    • Two-dimensional interaction of internal solitary waves in a two-layer fluid
    • Tsuji H., and Oikawa M. Two-dimensional interaction of internal solitary waves in a two-layer fluid. J. Phys. Soc. Japan 62 (1993) 3881-3892
    • (1993) J. Phys. Soc. Japan , vol.62 , pp. 3881-3892
    • Tsuji, H.1    Oikawa, M.2
  • 102
    • 0035483935 scopus 로고    scopus 로고
    • Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth
    • Tsuji H., and Oikawa M. Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth. Fluid Dyn. Res. 29 (2001) 251-267
    • (2001) Fluid Dyn. Res. , vol.29 , pp. 251-267
    • Tsuji, H.1    Oikawa, M.2
  • 103
    • 20444387964 scopus 로고    scopus 로고
    • Two-dimensional interaction of solitary waves in a modified Kadomtsev-Petviashvili equation
    • Tsuji H., and Oikawa M. Two-dimensional interaction of solitary waves in a modified Kadomtsev-Petviashvili equation. J. Phys. Soc. Japan 73 (2004) 3034-3043
    • (2004) J. Phys. Soc. Japan , vol.73 , pp. 3034-3043
    • Tsuji, H.1    Oikawa, M.2
  • 104
    • 33750356794 scopus 로고    scopus 로고
    • Tsuji, H., Oikawa, M., 2006. Oblique interaction of solitary waves in a extended Kadomtsev-Petviashvili equation, in preparation.
  • 105
    • 0007827705 scopus 로고
    • Resonant interaction of cylindrical ion-acoustic solitons
    • Tsukabayashi I., and Nakamura Y. Resonant interaction of cylindrical ion-acoustic solitons. Phys. Lett. A 83 (1981) 151-154
    • (1981) Phys. Lett. A , vol.83 , pp. 151-154
    • Tsukabayashi, I.1    Nakamura, Y.2
  • 106
    • 0347821899 scopus 로고
    • The exact solution of the modified Korteweg-de Vries equation
    • Wadati M. The exact solution of the modified Korteweg-de Vries equation. J. Phys. Soc. Japan 32 (1972) 1681
    • (1972) J. Phys. Soc. Japan , vol.32 , pp. 1681
    • Wadati, M.1
  • 107
    • 0007690397 scopus 로고
    • The modified Korteweg-de Vries equation
    • Wadati M. The modified Korteweg-de Vries equation. J. Phys. Soc. Japan 34 (1973) 1289-1296
    • (1973) J. Phys. Soc. Japan , vol.34 , pp. 1289-1296
    • Wadati, M.1
  • 108
    • 0021392203 scopus 로고
    • Ion acoustic soliton in plasma with negative ion
    • Watanabe S. Ion acoustic soliton in plasma with negative ion. J. Phys. Soc. Japan 53 (1984) 950-956
    • (1984) J. Phys. Soc. Japan , vol.53 , pp. 950-956
    • Watanabe, S.1
  • 109
    • 36749112076 scopus 로고
    • The Painlevé property for partial differential equations
    • Weiss J., Tabor M., and Carnevale G. The Painlevé property for partial differential equations. J. Math. Phys. 24 (1983) 522-526
    • (1983) J. Math. Phys. , vol.24 , pp. 522-526
    • Weiss, J.1    Tabor, M.2    Carnevale, G.3
  • 110
    • 0001463054 scopus 로고
    • Interaction of ion-acoustic solitons in three-dimensional space
    • Yajima N., Oikawa M., and Satsuma J. Interaction of ion-acoustic solitons in three-dimensional space. J. Phys. Soc. Japan 44 (1978) 1711-1714
    • (1978) J. Phys. Soc. Japan , vol.44 , pp. 1711-1714
    • Yajima, N.1    Oikawa, M.2    Satsuma, J.3
  • 111
    • 0001774896 scopus 로고
    • A synergetic approach to problems of nonlinear dispersive wave propagation and interaction
    • Ames W.F. (Ed), Academic Press, New York
    • Zabusky N.J. A synergetic approach to problems of nonlinear dispersive wave propagation and interaction. In: Ames W.F. (Ed). Nonlinear Partial Differential Equations (1967), Academic Press, New York 223-258
    • (1967) Nonlinear Partial Differential Equations , pp. 223-258
    • Zabusky, N.J.1
  • 112
    • 33846361348 scopus 로고
    • Interaction of "solitons" in a collisionless plasma and the recurrence of initial states
    • Zabusky N.J., and Kruskal M.D. Interaction of "solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-243
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 113
    • 0040761535 scopus 로고
    • Formation of stationary nonlinear waves by superposition of solitons
    • Zaitsev A.A. Formation of stationary nonlinear waves by superposition of solitons. Sov. Phys. Dokl. 28 (1983) 720-722
    • (1983) Sov. Phys. Dokl. , vol.28 , pp. 720-722
    • Zaitsev, A.A.1
  • 114
    • 0009372301 scopus 로고
    • A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
    • Zakharov V.E., and Shabat A.B. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I. Funct. Anal. Appl. 8 (1974) 226-235
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 226-235
    • Zakharov, V.E.1    Shabat, A.B.2
  • 115
    • 0001489237 scopus 로고
    • Inelastic collision of spherical ion-acoustic solitons
    • Ze F., Hershkowitz N., Chan C., and Lonngren K.E. Inelastic collision of spherical ion-acoustic solitons. Phys. Rev. Lett. 42 (1979) 1747-1750
    • (1979) Phys. Rev. Lett. , vol.42 , pp. 1747-1750
    • Ze, F.1    Hershkowitz, N.2    Chan, C.3    Lonngren, K.E.4
  • 116
    • 0007827564 scopus 로고
    • Oblique collision of ion-acoustic solitons
    • Ze F., Hershkowitz N., and Lonngren K.E. Oblique collision of ion-acoustic solitons. Phys. Fluids 23 (1980) 1155-1163
    • (1980) Phys. Fluids , vol.23 , pp. 1155-1163
    • Ze, F.1    Hershkowitz, N.2    Lonngren, K.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.