Multiple-soliton solutions for a (3+1)-dimensional generalized KP equation

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 2, 2012, Pages 491-495

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Generalized KP equation; Multiple soliton solutions; Simplified Hirota's method

Indexed keywords

AM GENERALS; FREE PARAMETERS; GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION; HIROTA METHOD; KADOMTSEV-PETVIASHVILI EQUATION; MULTIPLE-SOLITON SOLUTIONS; SIMPLIFIED HIROTUM METHOD; SINGULAR SOLITON SOLUTIONS; SPATIAL VARIABLES;

SOLITONS;

EID: 80052378401     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.05.025     Document Type: Article

References (24)

1. Hirota R. The direct method in soliton theory 2004, Cambridge University Press, Cambridge.
2. Hirota R., Ito M. Resonance of solitons in one dimension. J Phys Soc Jpn 1983, 52(3):744-748.
3. Hirota R., Satsuma J. N-soliton solutions of model equations for shallow water waves. J Phys Soc Jpn 1976, 40(2):611-612.
4. Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Progress Theor Phys 1974, 52(5):1498-1512.
5. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett 1971, 27(18):1192-1194.
6. Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations. J Math Phys 1987, 28(8):1732-1742.
7. Kobayashi T., Toda K. The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients. Symm Integr Geom: Methods Appl 2006, 2:1-10.
8. Hu X.-B., Wang D.-L., Tam H.-W., Xue W.-M. Soliton solutions to the Jimbo-Miwa equation and the Fordy-Gibbons-Jimbo-Miwa equation. Phys lett A 1999, 262:310-320.
9. Liu X.-Q., Jiang S. New solutions of the (3+1)-dimensional Jimbo-Miwa equation. Appl Math Comput 2004, 158:177-184.
10. Wang D., Sun W., Kong C., Zhang H. New extended rational expansion method and exact solutions of Boussinesq equation and Jimbo-Miwa equations. Appl Math Comput 2007, 189:878-886.
11. Ma W.X., Fan E. Linear superposition principle applying to Hirota bilinear equations. Comput math Appl 2011, 61:950-959.
12. Ma W.X., Abdeljabbar A., Asaad M.G. Wronskina and Grammian solutions to a (3+1)-dimensional generalized KP equation. Appl Math Comput 2011, in Press.
13. Kichenassamy S., Olver P. Existence and nonexistence of solitary wave solutions to higher-order model evolution equations. SIAM J Math Anal 1992, 23(5):1141-1166.
14. Hereman W., Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math Comput Simul 1997, 43:13-27.
15. Malfliet W., Hereman W. The tanh method: I. exact solutions of nonlinear evolution and wave equations. Phys Script 1996, 54:563-568.
16. Malfliet W., Hereman W. The tanh method: II. Perturbation technique for conservative systems. Phys Script 1996, 54:569-575.
17. Wazwaz A.M. Partial differential equations and solitary waves theorem 2009, Springer and HEP, Berlin.
18. Wazwaz A.M. Partial differential equations: methods and applications 2002, Balkema Publishers, The Netherlands.
19. Wazwaz A.M. N-soliton solutions for the Vakhnenko equation and its generalized forms. Phys Scr 2010, 82:065006.
20. Wazwaz A.M. A new generalized fifth-order nonlinear integrable equation. Phys Scr 2011, 83:035003.
21. Wazwaz A.M. Distinct variants of the KdV equation with compact and noncompact structures. Appl Math Comput 2004, 150:365-377.
22. Wazwaz A.M. New solitons and kinks solutions to the Sharma-Tasso-Olver equation. Appl Math Comput 2007, 188:1205-1213.
23. Ma W.-X., Lee J.-H. A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation. Chaos Solitons Fract 2009, 42:1356-1363.
24. Ma W.-X., Huang T., Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Phys Script 2010, 82:065003. 8pp.