A new (2+1)-dimensional Korteweg-de Vries equation and its extension to a new (3+1)-dimensional Kadomtsev-Petviashvili equation

Physica Scripta

Volumn 84, Issue 3, 2011, Pages

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

KADOMTSEV-PETVIASHVILI EQUATION; KDV EQUATIONS; KORTEWEG-DE VRIES EQUATIONS; MULTIPLE-SOLITON SOLUTIONS; RESONANCE PHENOMENA;

SOLITONS;

WAVE EQUATIONS;

EID: 80052684127     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/84/03/035010     Document Type: Article

References (27)

1. Peng Y Z 2010 A new (2+1)-dimensional KdV equation and its localized structures Commun. Theor. Phys. 54 863-5
2. Boiti M, Leon J and Pempinelli F 1987 Integrable two-dimensional generalisation of the sine- and sinh-Gordon equations Inverse Problems 3 37-49
3. Geng X and Ma Y 2007 N-soliton solution and its Wronskian form of a (2+1)-dimensional nonlinear evolution equation Phys. Lett. A 369 285-9
4. Wu J 2008 N-soliton solution, generalized double Wronskian determinant solution and rational solution for a (2+1)-dimensional nonlinear evolution equation Phys. Lett. A 373 83-8
5. Kadomtsev B B and Petviashvili V I 1970 On the stability of solitary waves in weakly dispersive media Sov. Phys. - Dokl. 15 539-41
6. Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
7. Hirota R 1974 A new form of Bäcklund transformations and its relation to the inverse scattering problem Prog. Theor. Phys. 52 1498-512
8. Hirota R 1971 Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons Phys. Rev. Lett. 27 1192-4
9. Hirota R and Ito M 1983 Resonance of solitons in one dimension J. Phys. Soc. Japan 52 744-8
10. Ito M 1980 An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order J. Phys. Soc. Japan 49 771-8
11. Ma W X and Fan E 2011 Linear superposition principle applying to Hirota bilinear equations Comput. Math. Appl. 61 950-9
12. Hietarinta J 1987 A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations J. Math. Phys. 28 1732-42
13. Hietarinta J 1987 A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations J. Math. Phys. 28 2094-101
14. Hereman W and Nuseir A 1997 Symbolic methods to construct exact solutions of nonlinear partial differential equations Math. Comput. Simul. 43 13-27 (Pubitemid 127454061)
15. Wazwaz A-M 2009 Four (2+1)-dimensional integrable extensions of the KdV equation: multiple-soliton and multiple singular soliton solutions Appl. Math. Comput. 215 1463-76
16. Wazwaz A-M 2007 Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method Appl. Math. Comput. 190 633-40 (Pubitemid 46856693)
17. Wazwaz A-M 2011 A new fifth-order nonlinear integrable equation: multiple soliton solutions Phys. Scr. 83 015012
18. Wazwaz A-M 2011 A new generalized fifth-order nonlinear integrable equation Phys. Scr. 83 035003
19. Wazwaz A-M 2007 Multiple-front solutions for the Burgers equation and the coupled Burgers equations Appl. Math. Comput. 190 1198-206 (Pubitemid 46935862)
20. Wazwaz A-M 2007 New solitons and kink solutions for the Gardner equation Commun. Nonlinear Sci. Numer. Simul. 12 1395-404 (Pubitemid 46832139)
21. Wazwaz A-M 2011 Integrability of coupled KdV equations Cent. Eur. J. Phys. 9 835-40
22. Wazwaz A-M 2007 Multiple-soliton solutions for the Boussinesq equation Appl. Math. Comput. 192 479-86 (Pubitemid 47445709)
23. Wazwaz A-M 2008 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. 199 133-8 (Pubitemid 351508321)
24. Wazwaz A-M 2008 Multiple-front solutions for the Burgers-Kadomtsev- Petvishvili equation Appl. Math. Comput. 200 437-43
25. Wazwaz A-M 2008 Multiple-soliton solutions for the Lax-Kadomtsev- Petvisahvili (Lax-KP) equation Appl. Math. Comput. 201 168-74
26. Wazwaz A-M 2008 The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves Appl. Math. Comput. 201 489-503
27. Wazwaz A-M 2008 Multiple-soliton solutions of two extended model equations for shallow water waves Appl. Math. Comput. 201 790-9