메뉴 건너뛰기




Volumn 16, Issue 5, 2003, Pages 819-839

Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; SOLITONS;

EID: 0037408898     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(02)00472-1     Document Type: Article
Times cited : (252)

References (66)
  • 4
    • 0033241374 scopus 로고    scopus 로고
    • Darboux transformation and solutions for an equation in 2+1 dimensions
    • Esteevez P.G. Darboux transformation and solutions for an equation in. 2+1 dimensions J Math Phys. 40:1999;1406-1419.
    • (1999) J Math Phys , vol.40 , pp. 1406-1419
    • Esteevez, P.G.1
  • 5
    • 0000017028 scopus 로고
    • Delta-dressing and exact solutions for the (2+1)-dimensional Harry Dym equation
    • Dubrousky V.G., Konopelchenko B.G. Delta-dressing and exact solutions for the (. 2+1 )-dimensional Harry Dym equation J Phys A. 27:1994;4719-4721.
    • (1994) J Phys A , vol.27 , pp. 4719-4721
    • Dubrousky, V.G.1    Konopelchenko, B.G.2
  • 6
    • 0034612891 scopus 로고    scopus 로고
    • Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation
    • Fan E.G. Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation. J Phys A. 33:2000;6925-6933.
    • (2000) J Phys A , vol.33 , pp. 6925-6933
    • Fan, E.G.1
  • 7
    • 18944408338 scopus 로고
    • Soliton solution of a coupled KdV equation
    • Hirota R., Satsuma J. Soliton solution of a coupled KdV equation. Phys Lett A. 85:1981;407-408.
    • (1981) Phys Lett A , vol.85 , pp. 407-408
    • Hirota, R.1    Satsuma, J.2
  • 8
    • 0034384726 scopus 로고    scopus 로고
    • The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited
    • Tam H.W., Ma W.X., Hu X.B., Wang D.L. The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited. J Phys Soc Jpn. 69:2000;45-51.
    • (2000) J Phys Soc Jpn , vol.69 , pp. 45-51
    • Tam, H.W.1    Ma, W.X.2    Hu, X.B.3    Wang, D.L.4
  • 13
    • 0035420587 scopus 로고    scopus 로고
    • Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
    • Alber M.S., Fedorov Y.N. Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians. Inverse Probl. 17:2001;1017-1042.
    • (2001) Inverse Probl , vol.17 , pp. 1017-1042
    • Alber, M.S.1    Fedorov, Y.N.2
  • 14
    • 0035981969 scopus 로고    scopus 로고
    • Algebro-geometric solution of the 2+1 dimensional Burgers equation with a discrete variable
    • Cao C.W., Geng X.G., Wang H.Y. Algebro-geometric solution of the. 2+1 dimensional Burgers equation with a discrete variable J Math Phys. 43:2002;621-643.
    • (2002) J Math Phys , vol.43 , pp. 621-643
    • Cao, C.W.1    Geng, X.G.2    Wang, H.Y.3
  • 15
    • 30244524644 scopus 로고    scopus 로고
    • Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
    • Wang M.L., Zhou Y.B., Li Z.B. Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys Lett A. 216:1996;67-75.
    • (1996) Phys Lett A , vol.216 , pp. 67-75
    • Wang, M.L.1    Zhou, Y.B.2    Li, Z.B.3
  • 16
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W. Solitary wave solutions of nonlinear wave equations. Am J Phys. 60:1992;650-654.
    • (1992) Am J Phys , vol.60 , pp. 650-654
    • Malfliet, W.1
  • 17
    • 0026413035 scopus 로고    scopus 로고
    • Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA
    • Hereman W. Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA. Comp Phys Commun. 65:1996;143-150.
    • (1996) Comp Phys Commun , vol.65 , pp. 143-150
    • Hereman, W.1
  • 18
    • 0030284901 scopus 로고    scopus 로고
    • An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations
    • Parkes E.J., Duffy B.R. An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations. Comput Phys Commun. 98:1996;288-300.
    • (1996) Comput Phys Commun , vol.98 , pp. 288-300
    • Parkes, E.J.1    Duffy, B.R.2
  • 19
    • 21344493193 scopus 로고
    • Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation
    • Parkes E.J. Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation. J Phys A. 27:1994;L497-L502.
    • (1994) J Phys A , vol.27
    • Parkes, E.J.1
  • 20
    • 0034606149 scopus 로고    scopus 로고
    • Extended tanh-function method and its applications to nonlinear equations
    • Fan E.G. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A. 277:2000;212-218.
    • (2000) Phys Lett A , vol.277 , pp. 212-218
    • Fan, E.G.1
  • 21
    • 0036498657 scopus 로고    scopus 로고
    • Travelling wave solutions for nonlinear equations using symbolic computation
    • Fan E.G. Travelling wave solutions for nonlinear equations using symbolic computation. Comput Math Appl. 43:2002;671-680.
    • (2002) Comput Math Appl , vol.43 , pp. 671-680
    • Fan, E.G.1
  • 22
    • 0037071122 scopus 로고    scopus 로고
    • New exact solutions for three evolution equations
    • Yao Y.X., Li Z.B. New exact solutions for three evolution equations. Phys Lett A. 297:2002;196-204.
    • (2002) Phys Lett A , vol.297 , pp. 196-204
    • Yao, Y.X.1    Li, Z.B.2
  • 23
    • 0000168251 scopus 로고    scopus 로고
    • Exact solitary wave and soliton solutions of the fifth order model equation
    • Li Z.B., Liu Y.P., Wang M.L. Exact solitary wave and soliton solutions of the fifth order model equation. Acta Math Sin. 22:2002;138-144.
    • (2002) Acta Math Sin , vol.22 , pp. 138-144
    • Li, Z.B.1    Liu, Y.P.2    Wang, M.L.3
  • 24
    • 0041762748 scopus 로고    scopus 로고
    • On exact quasistationary solutions to a nonlinear reaction-diffusion equation
    • Samsonov A.M. On exact quasistationary solutions to a nonlinear reaction-diffusion equation. Phys Lett A. 245:1998;527-536.
    • (1998) Phys Lett A , vol.245 , pp. 527-536
    • Samsonov, A.M.1
  • 25
    • 36149030679 scopus 로고
    • Exact travelling wave solutions of nonlionear evolution equation of surface-waves in a convecting fluid
    • Porubov A.V. Exact travelling wave solutions of nonlionear evolution equation of surface-waves in a convecting fluid. J Phys A. 26:1993;L797-L800.
    • (1993) J Phys A , vol.26
    • Porubov, A.V.1
  • 26
    • 0000346840 scopus 로고    scopus 로고
    • Some general periodic solutions to coupled nonlinear Schrodinger equations
    • Porubov A.V., Paeker D.F. Some general periodic solutions to coupled nonlinear Schrodinger equations. Wave Motion. 29:1999;97-109.
    • (1999) Wave Motion , vol.29 , pp. 97-109
    • Porubov, A.V.1    Paeker, D.F.2
  • 27
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • Liu S.K., Fu Z.T., Liu S.D., Zhao Q. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys Lett A. 289:2001;69-74.
    • (2001) Phys Lett A , vol.289 , pp. 69-74
    • Liu, S.K.1    Fu, Z.T.2    Liu, S.D.3    Zhao, Q.4
  • 28
    • 0347687520 scopus 로고    scopus 로고
    • New periodic solutions to a kind of nonlinear wave equations
    • Liu S.K., Fu Z.T., Liu S.D., Zhao Q. New periodic solutions to a kind of nonlinear wave equations. Acta Phys Sin. 51:2002;10-14.
    • (2002) Acta Phys Sin , vol.51 , pp. 10-14
    • Liu, S.K.1    Fu, Z.T.2    Liu, S.D.3    Zhao, Q.4
  • 31
    • 77952771289 scopus 로고
    • Wave-propagation in nonlinear lattice
    • Wadati M. Wave-propagation in nonlinear lattice. J Phys Soc Jpn. 38:1975;673-680.
    • (1975) J Phys Soc Jpn , vol.38 , pp. 673-680
    • Wadati, M.1
  • 32
    • 84988146340 scopus 로고
    • Exact solutions to the combined KdV and MKdV equation
    • Mohamad M.N.B. Exact solutions to the combined KdV and MKdV equation. Math Meth Appl Sci. 15:1992;73-78.
    • (1992) Math Meth Appl Sci , vol.15 , pp. 73-78
    • Mohamad, M.N.B.1
  • 33
    • 0032378150 scopus 로고    scopus 로고
    • New solitary wave solution of the combined KdV and mKdV equation
    • Zhang J. New solitary wave solution of the combined KdV and mKdV equation. Int J Theor Phys. 37:1998;1541-1546.
    • (1998) Int J Theor Phys , vol.37 , pp. 1541-1546
    • Zhang, J.1
  • 34
    • 0034506466 scopus 로고    scopus 로고
    • Exact solitary wave solutions to a combined KdV and mKdV eqation
    • Yu J. Exact solitary wave solutions to a combined KdV and mKdV eqation. Math Meth Appl Sci. 23:2000;1667-1670.
    • (2000) Math Meth Appl Sci , vol.23 , pp. 1667-1670
    • Yu, J.1
  • 35
    • 2242431794 scopus 로고    scopus 로고
    • New types of solitary-wave solutions from the combined KdV-mKdV equation
    • Hong W.P. New types of solitary-wave solutions from the combined KdV-mKdV equation. Nuovo Cimento B. 115:2000;117-118.
    • (2000) Nuovo Cimento B , vol.115 , pp. 117-118
    • Hong, W.P.1
  • 36
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa R., Holm D.D. An integrable shallow water equation with peaked solitons. Phys Rev Lett. 71:1993;1661-1664.
    • (1993) Phys Rev Lett , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 37
    • 49049150360 scopus 로고
    • Syplectic structures, their Backlund transformations and hereditary symmetries
    • Fuchssteiner B., Fokas A.S. Syplectic structures, their Backlund transformations and hereditary symmetries. Physica D. 4:1981;47-66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 38
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • Fuchssteiner B. Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation. Physica D. 95:1996;229-243.
    • (1996) Physica D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 39
    • 0004456042 scopus 로고    scopus 로고
    • Transformations for the Camassa-Holm equation, its high-frequency limit and the Sinh-Gordon equation
    • Dai H.H., Pavlov M. Transformations for the Camassa-Holm equation, its high-frequency limit and the Sinh-Gordon equation. J Phys Soc Jpn. 67:1998;3655-3657.
    • (1998) J Phys Soc Jpn , vol.67 , pp. 3655-3657
    • Dai, H.H.1    Pavlov, M.2
  • 40
    • 0035873662 scopus 로고    scopus 로고
    • The spectral problem and particular solutions to the (2+1)-dimensional integrable generalization of the Camassa-Holm equation
    • Zenchuk A.I. The spectral problem and particular solutions to the (2+1 )-dimensional integrable generalization of the Camassa-Holm equation Physica D. 152-153:2001;178-188.
    • (2001) Physica D , vol.152-153 , pp. 178-188
    • Zenchuk, A.I.1
  • 41
    • 0000259839 scopus 로고    scopus 로고
    • Nonlinear superposition formula for the Kaup-Kupershmidt partial differential equation
    • Musette M., Verhoeven C. Nonlinear superposition formula for the Kaup-Kupershmidt partial differential equation. Physica D. 144:2000;211-220.
    • (2000) Physica D , vol.144 , pp. 211-220
    • Musette, M.1    Verhoeven, C.2
  • 42
    • 0035419947 scopus 로고    scopus 로고
    • A reformulation of the 'dressing method' for the Sawada-Kotera equation
    • Parker A. A reformulation of the 'dressing method' for the Sawada-Kotera equation. Inverse Probl. 17:2001;885-895.
    • (2001) Inverse Probl , vol.17 , pp. 885-895
    • Parker, A.1
  • 43
    • 0345846114 scopus 로고    scopus 로고
    • On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave
    • Parker A. On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave. Physica D. 137:2000;25-33.
    • (2000) Physica D , vol.137 , pp. 25-33
    • Parker, A.1
  • 44
    • 4243340827 scopus 로고
    • Some new integrable nonlinear evolution equation
    • Konopelchenko B.G., Dubrovsky V. Some new integrable nonlinear evolution equation. Phys Lett A. 75:1980;325.
    • (1980) Phys Lett A , vol.75 , pp. 325
    • Konopelchenko, B.G.1    Dubrovsky, V.2
  • 45
    • 0000728855 scopus 로고    scopus 로고
    • Soliton solutions and symmetries of the 2+1 dimensional Kaup-Kupershmidt equation
    • Hu X.B., Wang D.L., Qian X.M. Soliton solutions and symmetries of the. 2+1 dimensional Kaup-Kupershmidt equation Phys Lett A. 262:1999;409-415.
    • (1999) Phys Lett A , vol.262 , pp. 409-415
    • Hu, X.B.1    Wang, D.L.2    Qian, X.M.3
  • 46
    • 18844473851 scopus 로고    scopus 로고
    • The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via partial derivative-dressing method
    • Dubrovsky V.G., Lisitsyn Y.V. The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via partial derivative-dressing method. Phys Lett A. 295:2002;198-207.
    • (2002) Phys Lett A , vol.295 , pp. 198-207
    • Dubrovsky, V.G.1    Lisitsyn, Y.V.2
  • 47
    • 34250384767 scopus 로고
    • Nonlinear evolution equations associated with energy dependent Schrodinger potentials
    • Jaulent M., Miodek K. Nonlinear evolution equations associated with energy dependent Schrodinger potentials. Lett Math Phys. 1:1976;43-250.
    • (1976) Lett Math Phys , vol.1 , pp. 43-250
    • Jaulent, M.1    Miodek, K.2
  • 48
    • 0035531337 scopus 로고    scopus 로고
    • Reduction of dispersionless coupled KdV equations to the Euler-Darboux equation
    • Matsuna Y. Reduction of dispersionless coupled KdV equations to the Euler-Darboux equation. J Math Phys. 42:2001;1744-1760.
    • (2001) J Math Phys , vol.42 , pp. 1744-1760
    • Matsuna, Y.1
  • 49
    • 0031518253 scopus 로고    scopus 로고
    • The finite-band solution of the Jaulent-Miodek equation
    • Zhou R.G. The finite-band solution of the Jaulent-Miodek equation. J Math Phys. 38:1997;2535-2546.
    • (1997) J Math Phys , vol.38 , pp. 2535-2546
    • Zhou, R.G.1
  • 50
    • 0002487561 scopus 로고    scopus 로고
    • Separability and dynamical r-matrix for the constrained flows of the Jaulent-Miodek hierarchy
    • Zeng Y.B. Separability and dynamical r-matrix for the constrained flows of the Jaulent-Miodek hierarchy. Phys Lett A. 216:1996;26-32.
    • (1996) Phys Lett A , vol.216 , pp. 26-32
    • Zeng, Y.B.1
  • 51
    • 0032372276 scopus 로고    scopus 로고
    • Lax representation, r-matrix method, and separation of variables for the Neumann-type restricted flow
    • Zhou R.G. Lax representation, r-matrix method, and separation of variables for the Neumann-type restricted flow. J Math Phys. 39:1998;2848-2858.
    • (1998) J Math Phys , vol.39 , pp. 2848-2858
    • Zhou, R.G.1
  • 52
    • 21144472674 scopus 로고
    • New symmetries of the Jaulent-Miodek hierarchy
    • Ruan H.Y., Lou S.Y. New symmetries of the Jaulent-Miodek hierarchy. J Phys Soc. 62:1993;1917-1921.
    • (1993) J Phys Soc , vol.62 , pp. 1917-1921
    • Ruan, H.Y.1    Lou, S.Y.2
  • 53
    • 0041894128 scopus 로고
    • Spectral transformation for a 2-spatial dimension extension of the dispersive long wave equation
    • Boiti M., Leon J.J.P., Pempinelli F. Spectral transformation for a 2-spatial dimension extension of the dispersive long wave equation. Inverse Probl. 3:1987;371-387.
    • (1987) Inverse Probl , vol.3 , pp. 371-387
    • Boiti, M.1    Leon, J.J.P.2    Pempinelli, F.3
  • 54
    • 44949287513 scopus 로고
    • Group theoretical analysis dispersive long wave equations in 2 space dimensions
    • Paquin G., Wintermitz P. Group theoretical analysis dispersive long wave equations in 2 space dimensions. Physica D. 46:1990;122-138.
    • (1990) Physica D , vol.46 , pp. 122-138
    • Paquin, G.1    Wintermitz, P.2
  • 55
    • 21144476516 scopus 로고
    • Nonclassical symmetry reductions for the disspersive wave equations in shallow water
    • Lou S.Y. Nonclassical symmetry reductions for the disspersive wave equations in shallow water. J Math Phys. 33:1992;4300-4305.
    • (1992) J Math Phys , vol.33 , pp. 4300-4305
    • Lou, S.Y.1
  • 56
    • 0032349555 scopus 로고    scopus 로고
    • A generalized Hirota equation in 2+1 dimensionas
    • Maccari A. A generalized Hirota equation in. 2+1 dimensionas J Math Phys. 39:1998;6547-6551.
    • (1998) J Math Phys , vol.39 , pp. 6547-6551
    • Maccari, A.1
  • 57
    • 0000492769 scopus 로고
    • Exact envelope-soliton solutions of a nonlinear wave equation
    • Hirota R. Exact envelope-soliton solutions of a nonlinear wave equation. J Math Phys. 14:1973;805-809.
    • (1973) J Math Phys , vol.14 , pp. 805-809
    • Hirota, R.1
  • 58
    • 0002085196 scopus 로고
    • Dromion like structures in the (2+1)-dimensional breaking soliton solution
    • Radha R., Lakshmanan M. Dromion like structures in the (. 2+1 )-dimensional breaking soliton solution Phys Lett A. 197:1995;7-12.
    • (1995) Phys Lett A , vol.197 , pp. 7-12
    • Radha, R.1    Lakshmanan, M.2
  • 59
    • 0030367604 scopus 로고    scopus 로고
    • On the dromion solutions of a (2+1)-dimensional KdV-type equation
    • Lou S.Y. On the dromion solutions of a (. 2+1 )-dimensional KdV-type equation Commun Theor Phys. 26:1996;487-490.
    • (1996) Commun Theor Phys , vol.26 , pp. 487-490
    • Lou, S.Y.1
  • 60
    • 0030509522 scopus 로고    scopus 로고
    • Aboundant symmetry structures of the breaking soliton equation
    • Lou S.Y. Aboundant symmetry structures of the breaking soliton equation. Commun Theor Phys. 26:1996;51-56.
    • (1996) Commun Theor Phys , vol.26 , pp. 51-56
    • Lou, S.Y.1
  • 61
    • 0036256017 scopus 로고    scopus 로고
    • On the coherent structures of (2+1)-dimensional breaking soliton equation
    • Ruan H.Y. On the coherent structures of (. 2+1 )-dimensional breaking soliton equation J Phys Soc. 71:2002;453-457.
    • (2002) J Phys Soc , vol.71 , pp. 453-457
    • Ruan, H.Y.1
  • 62
    • 0035277264 scopus 로고    scopus 로고
    • Josephson vortex in a ratchet potential
    • 03111
    • Goldobin E., Sterck A., Koelle D. Josephson vortex in a ratchet potential. Phys Rev E. 63(03111):2001.
    • (2001) Phys Rev E , vol.63
    • Goldobin, E.1    Sterck, A.2    Koelle, D.3
  • 65
    • 0003147336 scopus 로고
    • Deforming some special solutions of the sine-Gordon equation to that of the double sine-Gordon equation
    • Lou S.Y., Ni G.J. Deforming some special solutions of the sine-Gordon equation to that of the double sine-Gordon equation. Phys Lett A. 140:1989;33-35.
    • (1989) Phys Lett A , vol.140 , pp. 33-35
    • Lou, S.Y.1    Ni, G.J.2
  • 66
    • 0000698750 scopus 로고    scopus 로고
    • Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
    • Gani V.A., Kudryavtsev A.E. Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies. Phys Rev E. 60:1999;3305-3309.
    • (1999) Phys Rev E , vol.60 , pp. 3305-3309
    • Gani, V.A.1    Kudryavtsev, A.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.