메뉴 건너뛰기




Volumn 211, Issue 2, 2009, Pages 495-501

Multiple-soliton solutions and multiple-singular soliton solutions for two higher-dimensional shallow water wave equations

Author keywords

Complete integrability; Hirota bilinear method; Multiple singular soliton solutions; Multiple soliton solutions

Indexed keywords

BILINEAR METHODS; COMPLETE INTEGRABILITY; DIRECT METHODS; HIROTA BILINEAR METHOD; INTEGRABLE EQUATIONS; MULTIPLE-SINGULAR SOLITON SOLUTIONS; MULTIPLE-SOLITON SOLUTIONS; SHALLOW WATER WAVE EQUATIONS;

EID: 64849094924     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.01.071     Document Type: Article
Times cited : (21)

References (22)
  • 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
    • 0001508211 scopus 로고
    • Exact solutions of the modified Korteweg-de Vries equation for multiple collisions of solitons
    • Hirota R. Exact solutions of the modified Korteweg-de Vries equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1456-1458
    • (1972) J. Phys. Soc. Jpn. , vol.33 , Issue.5 , pp. 1456-1458
    • Hirota, R.1
  • 8
    • 0001508212 scopus 로고
    • Exact solutions of the Sine-Gordon equation for multiple collisions of solitons
    • Hirota R. Exact solutions of the Sine-Gordon equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1459-1463
    • (1972) J. Phys. Soc. Jpn. , vol.33 , Issue.5 , pp. 1459-1463
    • Hirota, R.1
  • 9
    • 0000293426 scopus 로고
    • Resonance of solitons in one dimension
    • Hirota R., and Ito M. Resonance of solitons in one dimension. J. Phys. Soc. Jpn. 52 3 (1983) 744-748
    • (1983) J. Phys. Soc. Jpn. , vol.52 , Issue.3 , pp. 744-748
    • Hirota, R.1    Ito, M.2
  • 10
    • 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
  • 11
    • 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
  • 13
    • 0030829213 scopus 로고    scopus 로고
    • Symbolic methods to construct exact solutions of nonlinear partial differential equations
    • Hereman W., and Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Sim. 43 (1997) 13-27
    • (1997) Math. Comput. Sim. , vol.43 , pp. 13-27
    • Hereman, W.1    Nuseir, A.2
  • 14
    • 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 and Fractals 13 2 (2002) 321-330
    • (2002) Chaos, Solitons and Fractals , vol.13 , Issue.2 , pp. 321-330
    • Wazwaz, A.M.1
  • 15
    • 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
  • 16
    • 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
  • 17
    • 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
  • 18
    • 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
  • 19
    • 50249112604 scopus 로고    scopus 로고
    • N-soliton solutions for the combined KdV-CDG equation and the KdV-Lax equation
    • Wazwaz A.M. N-soliton solutions for the combined KdV-CDG equation and the KdV-Lax equation. Appl. Math. Comput. 203 (2008) 402-407
    • (2008) Appl. Math. Comput. , vol.203 , pp. 402-407
    • Wazwaz, A.M.1
  • 20
    • 51549107742 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equation
    • Wazwaz A.M. Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equation. Appl. Math. Comput. 203 (2008) 592-597
    • (2008) Appl. Math. Comput. , vol.203 , pp. 592-597
    • Wazwaz, A.M.1
  • 21
    • 52049108926 scopus 로고    scopus 로고
    • Single and multiple-soliton solutions for the (2 + 1)-dimensional KdV equation
    • Wazwaz A.M. Single and multiple-soliton solutions for the (2 + 1)-dimensional KdV equation. Appl. Math. Comput. 204 1 (2008) 20-26
    • (2008) Appl. Math. Comput. , vol.204 , Issue.1 , pp. 20-26
    • Wazwaz, A.M.1
  • 22
    • 52049114674 scopus 로고    scopus 로고
    • Solitons and singular solitons for the Gardner-KP equation
    • Wazwaz A.M. Solitons and singular solitons for the Gardner-KP equation. Appl. Math. Comput. 204 1 (2008) 162-169
    • (2008) Appl. Math. Comput. , vol.204 , Issue.1 , pp. 162-169
    • Wazwaz, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.