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Volumn 202, Issue 1, 2008, Pages 275-286

Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and Exp-function method

Author keywords

Exp function method; Generalized shallow water wave equation; Hirota bilinear method; Multiple soliton solutions; tanh coth method

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; LINEAR EQUATIONS; SOLITONS; WAVE EQUATIONS; WAVES;

EID: 46749141650     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.02.013     Document Type: Article
Times cited : (74)

References (38)
  • 1
    • 0000174288 scopus 로고
    • On a shallow water wave equation
    • Clarkson P.A., and Mansfield E.L. On a shallow water wave equation. Nonlinearity 7 (1994) 975-1000
    • (1994) Nonlinearity , vol.7 , pp. 975-1000
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 2
    • 0016369301 scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • Ablowitz M.J., Kaup D.J., Newell A.C., and Segur H. The inverse scattering transform - Fourier analysis for nonlinear problems. Stud. Appl. Math. 53 (1974) 249-315
    • (1974) Stud. Appl. Math. , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 3
    • 56249128025 scopus 로고
    • N-soliton solutions of model equations for shallow water waves
    • Hirota R., and Satsuma J. N-soliton solutions of model equations for shallow water waves. J. Phys. Soc. Jpn. 40 2 (1976) 611-612
    • (1976) J. Phys. Soc. Jpn. , vol.40 , Issue.2 , pp. 611-612
    • Hirota, R.1    Satsuma, J.2
  • 4
    • 0001247353 scopus 로고
    • A new form of Bäcklund transformations and its relation to the inverse scattering problem
    • Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Prog. Theor. Phys. 52 5 (1974) 1498-1512
    • (1974) Prog. Theor. Phys. , vol.52 , Issue.5 , pp. 1498-1512
    • Hirota, R.1
  • 6
    • 35949040541 scopus 로고
    • Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons
    • Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
    • (1971) Phys. Rev. Lett. , vol.27 , Issue.18 , pp. 1192-1194
    • Hirota, R.1
  • 7
    • 0001486467 scopus 로고
    • A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations
    • Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations. J. Math. Phys. 28 8 (1987) 1732-1742
    • (1987) J. Math. Phys. , vol.28 , Issue.8 , pp. 1732-1742
    • Hietarinta, J.1
  • 8
    • 0039623545 scopus 로고
    • A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations
    • Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations. J. Math. Phys. 28 9 (1987) 2094-2101
    • (1987) J. Math. Phys. , vol.28 , Issue.9 , pp. 2094-2101
    • Hietarinta, J.1
  • 11
    • 46749131975 scopus 로고    scopus 로고
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 22-26, 1991.
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 22-26, 1991.
  • 12
    • 0000531288 scopus 로고
    • An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order
    • Ito M. An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Jpn. 49 2 (1980) 771-778
    • (1980) J. Phys. Soc. Jpn. , vol.49 , Issue.2 , pp. 771-778
    • Ito, M.1
  • 13
    • 0001395372 scopus 로고
    • A method for finding N-soliton solutions of the KdV equation and KdV-like equation
    • Sawada K., and Kotera T. A method for finding N-soliton solutions of the KdV equation and KdV-like equation. Prog. Theor. Phys. 51 (1974) 1355-1367
    • (1974) Prog. Theor. Phys. , vol.51 , pp. 1355-1367
    • Sawada, K.1    Kotera, T.2
  • 14
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax P.D. Integrals of nonlinear equations of evolution and solitary waves. Commun. Pure Appl. Math. 21 (1968) 467-490
    • (1968) Commun. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 16
    • 1442264988 scopus 로고    scopus 로고
    • The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations
    • Malfliet W. The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 164-165 (2004) 529-541
    • (2004) J. Comput. Appl. Math. , vol.164-165 , pp. 529-541
    • Malfliet, W.1
  • 17
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
    • (1992) Am. J. Phys. , vol.60 , Issue.7 , pp. 650-654
    • Malfliet, W.1
  • 18
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method: I. Exact solutions of nonlinear evolution and wave equations
    • Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
    • (1996) Phys. Scripta , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.2
  • 19
    • 0000068096 scopus 로고    scopus 로고
    • The tanh method: II. Perturbation technique for conservative systems
    • Malfliet W., and Hereman W. The tanh method: II. Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575
    • (1996) Phys. Scripta , vol.54 , pp. 569-575
    • Malfliet, W.1    Hereman, W.2
  • 20
    • 3042750187 scopus 로고    scopus 로고
    • The tanh method for travelling wave solutions of nonlinear equations
    • Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
    • (2004) Appl. Math. Comput. , vol.154 , Issue.3 , pp. 713-723
    • Wazwaz, A.M.1
  • 22
    • 36749095116 scopus 로고    scopus 로고
    • The tanh-coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations
    • Wazwaz A.M. The tanh-coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations. Appl. Math. Comput. 195 (2008) 24-33
    • (2008) Appl. Math. Comput. , vol.195 , pp. 24-33
    • Wazwaz, A.M.1
  • 23
    • 33846641360 scopus 로고    scopus 로고
    • The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
    • Wazwaz A.M. The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. Appl. Math. Comput. 184 2 (2007) 1002-1014
    • (2007) Appl. Math. Comput. , vol.184 , Issue.2 , pp. 1002-1014
    • Wazwaz, A.M.1
  • 24
    • 34248229664 scopus 로고    scopus 로고
    • The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
    • Wazwaz A.M. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput. 188 (2007) 1467-1475
    • (2007) Appl. Math. Comput. , vol.188 , pp. 1467-1475
    • Wazwaz, A.M.1
  • 25
    • 0036462771 scopus 로고    scopus 로고
    • New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n) equations
    • Wazwaz A.M. New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n) equations. Chaos Solitons Fract. 13 2 (2002) 321-330
    • (2002) Chaos Solitons Fract. , vol.13 , Issue.2 , pp. 321-330
    • Wazwaz, A.M.1
  • 26
    • 34249786250 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
    • Wazwaz A.M. Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method. Appl. Math. Comput. 190 (2007) 633-640
    • (2007) Appl. Math. Comput. , vol.190 , pp. 633-640
    • Wazwaz, A.M.1
  • 27
    • 34247562366 scopus 로고    scopus 로고
    • The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation
    • Wazwaz A.M. The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation. Phys. Lett. A 366 1/2 (2007) 85-90
    • (2007) Phys. Lett. A , vol.366 , Issue.1-2 , pp. 85-90
    • Wazwaz, A.M.1
  • 28
    • 34250643151 scopus 로고    scopus 로고
    • Multiple-front solutions for the Burgers equation and the coupled Burgers equations
    • Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
    • (2007) Appl. Math. Comput. , vol.190 , pp. 1198-1206
    • Wazwaz, A.M.1
  • 29
    • 34249786250 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
    • Wazwaz A.M. Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method. Appl. Math. Comput. 190 (2007) 633-640
    • (2007) Appl. Math. Comput. , vol.190 , pp. 633-640
    • Wazwaz, A.M.1
  • 30
    • 34250643151 scopus 로고    scopus 로고
    • Multiple-front solutions for the Burgers equation and the coupled Burgers equations
    • Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
    • (2007) Appl. Math. Comput. , vol.190 , pp. 1198-1206
    • Wazwaz, A.M.1
  • 31
    • 34548823237 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the Boussinesq equation
    • Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486
    • (2007) Appl. Math. Comput. , vol.192 , pp. 479-486
    • Wazwaz, A.M.1
  • 32
    • 41949134292 scopus 로고    scopus 로고
    • The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
    • Wazwaz A.M. The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation. Appl. Math. Comput. 199 1 (2008) 133-138
    • (2008) Appl. Math. Comput. , vol.199 , Issue.1 , pp. 133-138
    • Wazwaz, A.M.1
  • 33
    • 43049165451 scopus 로고    scopus 로고
    • Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation
    • Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl. Math. Comput. 200 1 (2008) 437-443
    • (2008) Appl. Math. Comput. , vol.200 , Issue.1 , pp. 437-443
    • Wazwaz, A.M.1
  • 34
    • 44649142146 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation
    • Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl. Math. Comput. 201 1-2 (2008) 166-174
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 166-174
    • Wazwaz, A.M.1
  • 35
    • 44649165713 scopus 로고    scopus 로고
    • The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves
    • Wazwaz A.M. The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves. Appl. Math. Comput. 201 1-2 (2008) 489-503
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 489-503
    • Wazwaz, A.M.1
  • 36
    • 44649179317 scopus 로고    scopus 로고
    • Multiple-soliton solutions of two extended model equations for shallow water waves
    • Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput. 201 1-2 (2008) 790-799
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 790-799
    • Wazwaz, A.M.1
  • 37
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.-H., and Wu X.-H. Exp-function method for nonlinear wave equations. Chaos Solitons Fract. 30 (2006) 700-708
    • (2006) Chaos Solitons Fract. , vol.30 , pp. 700-708
    • He, J.-H.1    Wu, X.-H.2
  • 38
    • 37249080286 scopus 로고    scopus 로고
    • Application of Exp-Function method to symmetric regularized long wave (SRLW) equation
    • Xu F. Application of Exp-Function method to symmetric regularized long wave (SRLW) equation. Phys. Lett. A 372 (2008) 252-257
    • (2008) Phys. Lett. A , vol.372 , pp. 252-257
    • Xu, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.