Regular soliton solutions and singular soliton solutions for the modified Kadomtsev-Petviashvili equations

Applied Mathematics and Computation

Volumn 204, Issue 1, 2008, Pages 227-232

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Hirota bilinear method; mKP equation; N soliton solutions; Singular soliton solutions

Indexed keywords

TURBULENT FLOW;

BILINEAR METHODS; HIROTA BILINEAR METHOD; INFINITE NUMBERS; INTEGRABLE EQUATIONS; KADOMTSEV-PETVIASHVILI EQUATIONS; MKP EQUATION; N-SOLITON SOLUTIONS; SINGULAR SOLITON SOLUTIONS; SOLITON SOLUTIONS;

SOLITONS;

EID: 52049098686     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.06.031     Document Type: Article

References (20)

1. Hirota R., and Ito M. Resonance of solitons in one dimension. J. Phys. Soc. Japan 52 3 (1983) 744-748
2. Ito M. An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Japan 49 2 (1980) 771-778
3. Hirota R., and Satsuma J. N-soliton solutions of model equations for shallow water waves. J. Phys. Soc. Japan 40 2 (1976) 611-612
4. Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Prog. Theor. Phys. 52 5 (1974) 1498-1512
5. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
6. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
7. 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
8. 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
9. W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: 13th World Congress on Computation and Applied Mathematics, vol. 2, 1991, pp. 842-863.
10. W. Hereman, W. Zhuang, Symbolic computation of solitons with Macsyma, Computational and Applied Mathematics II: Differential Equations, 1992, pp. 287-296.
11. W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 1991, pp. 22-26.
12. 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
13. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
14. Wazwaz A.M. New solitons and kink solutions for the Gardner equation. Commun. Nonlinear Sci. Numerical Simulation 12 8 (2007) 1395-1404
15. Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486
16. 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
17. Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl. Math. Comput. 200 (2008) 437-443
18. Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl. Math. Comput. 201 1/2 (2008) 168-174
19. 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
20. Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput. 201 1/2 (2008) 790-799