A study on two extensions of the Bogoyavlenskii-Schieff equation

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 4, 2012, Pages 1500-1505

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Bogoyavlenskii Schieff equation; Multiple soliton solutions; The simplified Hirota's method

Indexed keywords

BOGOYAVLENSKII-SCHIEFF EQUATION; HIROTA METHOD; INTEGRABILITY; MULTIPLE-SOLITON SOLUTIONS; N-SOLITON SOLUTIONS; THE SIMPLIFIED HIROTUM METHOD;

SOLITONS;

EID: 80054967233     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.08.027     Document Type: Article

References (31)

1. Song-Ju Y., Toda K., Fukuyama T. N-soliton solutions to a new (2+1) dimensional integrable equation. Physics A: Math Gen 1998, 31(50):10181.
2. Toda K., Song-Ju Y., Fukuyama T. The Bogoyavlenskii-Schiff hierarchy and integrable equation in (2+1)-dimensions. Rep Math Phys 1999, 44:247-254.
3. Song-Ju Y, Toda K, Fukuyama T. Hierarchy of higher dimensional integrable equation; 1998. arxiv:solv-int/9802005v1.
4. Bogoyavlenskii O.I. Overturning solitons in new two-dimensional integrable equations. Math Izvestiya 1990, 34:2-245.
5. Bogoyavlenskii O.I. Breaking solitons in (2+1)-dimensional integrable equations. Russian Math Surv 1990, 45:1-86.
6. Schiff J. Painleve transcendents: their asymptotics and physical applications 1992, Plenum, New York.
7. Wazwaz A.M. Multiple soliton solutions for the Bogoyavlenskii's generalized breaking soliton equations and its extension form. Appl Math Comput 2010, 217(8):4282-4288.
8. Hirota R., Ito M. Resonance of solitons in one dimension. J Phys Soc Jpn 1983, 52(3):744-748.
9. Hirota R. The direct method in soliton theory 2004, Cambridge University Press, Cambridge.
10. 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.
11. Hereman W., Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math Comput Simul 1997, 43:13-27.
12. Wazwaz A.M. Integrable (2+1)-dimensional and (3+1)-dimensional breaking soliton equations. Phys Scr 2010, 81:035005.
13. Wazwaz A.M. Partial differential equations and solitary waves theory 2009, HEP and Springer, Peking and Berlin.
14. Wazwaz A.M. M-component nonlinear evolution equations: multiple soliton solutions. Phys Scr 2010, 81:055004.
15. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl Math Comput 2007, 190:1198-1206.
16. Wazwaz A.M. New solitons and kink solutions for the Gardner equation. Commun Nonlinear Sci Numer Simul 2007, 12(8):1395-1404.
17. Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl Math Comput 2007, 192:479-486.
18. 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 2008, 199(1):133-138.
19. Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl Math Comput 2008, 200:437-443.
20. Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl Math Comput 2008, 201(1/2):168-174.
21. Wazwaz A.M. The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves. Appl Math Comput 2008, 201(1/2):489-503.
22. Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl Math Comput 2008, 201(1/2):790-799.
23. Wazwaz A.M. Single and multiple-soliton solutions for the (2+1)-dimensional KdV equation. Appl Math Comput 2008, 204:20-26.
24. Wazwaz A.M. Solitons and singular solitons for the Gardner-KP equation. Appl Math Comput 2008, 204:162-169.
25. Wazwaz A.M. Regular soliton solutions and singular soliton solutions for the modified Kadomtsev-Petviashvili equations. Appl Math Comput 2008, 204:817-823.
26. Wazwaz A.M. Multiple kink solutions and multiple singular kink solutions for the (2+1)-dimensional Burgers equations. Appl Math Comput 2008, 204:529-541.
27. Ma W.-X. Complexiton solutions of the Kortewegde Vries equation. Phys Lett A 2002, 301:35-44.
28. Ma W.-X. Complexiton solutions of the Kortewegde Vries equation with self-consistent sources. Chaos Solitons Fract 2005, 26:1453-1458.
29. Ma W.-X., Fan E. Linear superposition principle applying to Hirota bilinear equations. Comput Math Appl 2011, 61:950-959.
30. Ma W.-X., Huang T., Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Phys Scr 2010, 82:065003. 8p.
31. Asaad MG, Ma W-X. Grammian solutions to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation and its modified counterpart. Appl Math Comput in press.