메뉴 건너뛰기




Volumn 105, Issue 4, 2000, Pages 385-403

Lump interactions and collapse in the modified Zakharov-Kuznetsov equation

Author keywords

[No Author keywords available]

Indexed keywords

KORTEWEG-DE VRIES EQUATION; MAGNETOPLASMA;

EID: 0038497346     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00157     Document Type: Article
Times cited : (29)

References (36)
  • 1
    • 0001379378 scopus 로고
    • Nonlinear evolution of disturbances in plasmas and other dispersive media
    • Y. A. BEREZIN and V. I. KARPMAN, Nonlinear evolution of disturbances in plasmas and other dispersive media, Sov. Phys. JETP 24:1049-1056 (1967).
    • (1967) Sov. Phys. JETP , vol.24 , pp. 1049-1056
    • Berezin, Y.A.1    Karpman, V.I.2
  • 2
    • 4243844357 scopus 로고
    • Propagation of ion-acoustic solitary waves of small amplitude
    • M. WASHIMI and T. TANIUTI, Propagation of ion-acoustic solitary waves of small amplitude, Phys. Rev. Lett. 17:996-998 (1966).
    • (1966) Phys. Rev. Lett. , vol.17 , pp. 996-998
    • Washimi, M.1    Taniuti, T.2
  • 4
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersive media
    • B. B. KADOMTSEV and V. I. PETVIASHVILI, On the stability of solitary waves in weakly dispersive media, Sov. Phys. Dokl. 15:539-541 (1970).
    • (1970) Sov. Phys. Dokl. , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 7
    • 0039297073 scopus 로고
    • Three-dimensional stability of korteweg de vries waves and solitons, III. Lagrangian methods, KdV with positive dispersion
    • E. INFELD, Three-dimensional stability of Korteweg de Vries waves and solitons, III. Lagrangian methods, KdV with positive dispersion, Acta Phys. Polon. A60:623-643 (1981).
    • (1981) Acta Phys. Polon. , vol.A60 , pp. 623-643
    • Infeld, E.1
  • 8
    • 0005238277 scopus 로고
    • Two-dimensional stability of ion acoustic solitons
    • M. KAKO and G. ROWLANDS, Two-dimensional stability of ion acoustic solitons, Plasma Phys. 18:165-170 (1976).
    • (1976) Plasma Phys. , vol.18 , pp. 165-170
    • Kako, M.1    Rowlands, G.2
  • 10
    • 77956809859 scopus 로고
    • Hydrodynamic stability of parallel flow of inviscid fluid
    • P. G. DRAZIN and L. N. HOWARD, Hydrodynamic stability of parallel flow of inviscid fluid, Adv. Appl. Math. 7:1-89 (1966).
    • (1966) Adv. Appl. Math. , vol.7 , pp. 1-89
    • Drazin, P.G.1    Howard, L.N.2
  • 11
    • 0022052359 scopus 로고
    • Self-focusing of nonlinear ion acoustic waves and solitons in magnetized plasmas
    • E. INFELD, Self-focusing of nonlinear ion acoustic waves and solitons in magnetized plasmas, J. Plasma Physics 33:171-182 (1985).
    • (1985) J. Plasma Physics , vol.33 , pp. 171-182
    • Infeld, E.1
  • 12
    • 0000985657 scopus 로고
    • Weak nonlinear hydromagnetic waves in a cold collision-free plasma
    • T. KAKUTANI and H. ONO, Weak nonlinear hydromagnetic waves in a cold collision-free plasma, J. Phys. Soc. Japan 26:1305-1318 (1965).
    • (1965) J. Phys. Soc. Japan , vol.26 , pp. 1305-1318
    • Kakutani, T.1    Ono, H.2
  • 14
    • 0024882276 scopus 로고
    • Collapsing states of generalized Korteweg-de Vries equations
    • R. BLAHA, E. W. LAEDKE, and K. H. SPATSCHEK, Collapsing states of generalized Korteweg-de Vries equations, Physica D 40:249-264 (1989).
    • (1989) Physica D , vol.40 , pp. 249-264
    • Blaha, R.1    Laedke, E.W.2    Spatschek, K.H.3
  • 16
    • 0000359675 scopus 로고    scopus 로고
    • An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations
    • D. E. PELINOVSKY and R. H. J. GRIMSHAW, An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations, Physica D 98:139-155 (1996).
    • (1996) Physica D , vol.98 , pp. 139-155
    • Pelinovsky, D.E.1    Grimshaw, R.H.J.2
  • 18
    • 0040482083 scopus 로고
    • The scalar field of a stationary nucleon in a non-linear theory
    • N. V. MITSKEVICH, The scalar field of a stationary nucleon in a non-linear theory, Sov. Phys. JETP 2:197-202 (1956).
    • (1956) Sov. Phys. JETP , vol.2 , pp. 197-202
    • Mitskevich, N.V.1
  • 19
    • 0040482084 scopus 로고
    • On a certain nonlinear differential equation
    • J. L. SYNGE, On a certain nonlinear differential equation, Proc. Roy. Irish Acad. 62:17-41 (1961).
    • (1961) Proc. Roy. Irish Acad. , vol.62 , pp. 17-41
    • Synge, J.L.1
  • 20
    • 0041076162 scopus 로고
    • Existence of stationary states in nonlinear scalar field equations
    • D. Reidel Publishing Company, Dordrecht, The Netherlands
    • H. BERESTYCKI and P. L. LIONS, Existence of stationary states in nonlinear scalar field equations, in Bifurcation Phenomena in Mathematical Physics and Related Topics, pp. 269-292, D. Reidel Publishing Company, Dordrecht, The Netherlands, 1980.
    • (1980) Bifurcation Phenomena in Mathematical Physics and Related Topics , pp. 269-292
    • Berestycki, H.1    Lions, P.L.2
  • 21
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • 3 = 0 and a variational characterization of other solutions, Arch. Rational Mech. Anal. 46:81-95 (1972).
    • (1972) Arch. Rational Mech. Anal. , vol.46 , pp. 81-95
    • Coffman, C.V.1
  • 23
    • 0007070254 scopus 로고
    • Asymptotic solutions of nonlinear second-order differential equations with variable coefficients
    • G. E. KUZMAK, Asymptotic solutions of nonlinear second-order differential equations with variable coefficients, PMM 23:515-526 (1959).
    • (1959) PMM , vol.23 , pp. 515-526
    • Kuzmak, G.E.1
  • 24
    • 0014838172 scopus 로고
    • The evolution of multiphase modes for nonlinear dispersive waves
    • M. J. ABLOWITZ and D. J. BENNEY, The evolution of multiphase modes for nonlinear dispersive waves, Stud. Appl. Math. 49:225-238 (1970).
    • (1970) Stud. Appl. Math. , vol.49 , pp. 225-238
    • Ablowitz, M.J.1    Benney, D.J.2
  • 25
    • 0000557030 scopus 로고
    • A perturbation method for nonlinear dispersive wave problems
    • J. C. LUKE, A perturbation method for nonlinear dispersive wave problems, Proc. Roy. Soc. A 292:403-412 (1966).
    • (1966) Proc. Roy. Soc. A , vol.292 , pp. 403-412
    • Luke, J.C.1
  • 26
    • 0001273346 scopus 로고
    • Nonlinear dispersive waves
    • G. B. WHITHAM, Nonlinear dispersive waves, Proc. Roy. Soc. London A 283:238-261 (1965).
    • (1965) Proc. Roy. Soc. London A , vol.283 , pp. 238-261
    • Whitham, G.B.1
  • 28
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear wave phenomena
    • B. FORNBERG and G. B. WHITHAM, A numerical and theoretical study of certain nonlinear wave phenomena, Phyl. Trans. Roy. Soc. Lond. A 289:373-404 (1978).
    • (1978) Phyl. Trans. Roy. Soc. Lond. A , vol.289 , pp. 373-404
    • Fornberg, B.1    Whitham, G.B.2
  • 29
  • 30
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear schrödinger equation at critical dimension
    • M. J. LANDMAN, G. C. PAPANICOLAOU, C. SULEM, and P. L. SULEM, Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension, Phys. Rev. A 38:3837-3843 (1988).
    • (1988) Phys. Rev. A , vol.38 , pp. 3837-3843
    • Landman, M.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 31
    • 45549111243 scopus 로고
    • Focusing and multifocusing solutions of the nonlinear Schrödinger equation
    • B. J. LEMESURIER, G. C. PAPANICOLAOU, C. SULEM, and P. L. SULEM, Focusing and multifocusing solutions of the nonlinear Schrödinger equation, Physica D 31:78-102 (1988).
    • (1988) Physica D , vol.31 , pp. 78-102
    • Lemesurier, B.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 32
    • 0001678668 scopus 로고
    • Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
    • B. J. LEMESURIER, G. C. PAPANICOLAOU, C. SULEM, and P. L. SULEM, Local structure of the self-focusing singularity of the nonlinear Schrödinger equation, Physica D 32:210-226 (1988).
    • (1988) Physica D , vol.32 , pp. 210-226
    • Lemesurier, B.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 33
    • 0006645185 scopus 로고
    • Stability of isotropic singularities for the nonlinear Schrödinger equation
    • M. J. LANDMAN, G. C. PAPANICOLAOU, C. SULEM, P. L. SULEM, and X. P. WANG, Stability of isotropic singularities for the nonlinear Schrödinger equation, Physica D 47:393-415 (1991).
    • (1991) Physica D , vol.47 , pp. 393-415
    • Landman, M.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4    Wang, X.P.5
  • 34
    • 0029104726 scopus 로고
    • Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation
    • J. L. BONA, V. A. DOUGALIS, O. A. KARAKASHIAN, and W. R. MCKINNEY, Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation, Phil. Trans. Roy. Soc. Lond. A 351:107-164 (1995).
    • (1995) Phil. Trans. Roy. Soc. Lond. A , vol.351 , pp. 107-164
    • Bona, J.L.1    Dougalis, V.A.2    Karakashian, O.A.3    McKinney, W.R.4
  • 35
    • 0000988035 scopus 로고
    • Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation
    • X. P. WANG, M. J. ABLOWITZ, and H. SEGUR, Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation, Physica D 78:241-265 (1994).
    • (1994) Physica D , vol.78 , pp. 241-265
    • Wang, X.P.1    Ablowitz, M.J.2    Segur, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.