Multiple-soliton solutions for the Lax-Kadomtsev-Petviashvili (Lax-KP) equation

Applied Mathematics and Computation

Volumn 201, Issue 1-2, 2008, Pages 168-174

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Hereman's method; Hirota bilinear method; KP equation; Lax equation; Multiple soliton solutions; tanh coth Method

Indexed keywords

PROBLEM SOLVING; SOLITONS;

KP EQUATION; LAX EQUATION; TANH-COTH METHOD;

INTEGRAL EQUATIONS;

EID: 44649142146     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.12.009     Document Type: Article

References (26)

1. Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Progr. Theo. Phys. 52 5 (1974) 1498-1512
2. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
3. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
4. 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
5. Hirota R. Exact solutions of the Sine-Gordon equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1459-1463
6. Lax P.D. Integrals of nonlinear equations of evolution and solitary waves. Commun. Pure Appl. Math. 21 (1968) 467-490
7. Kadomtsev B.B., and Petviashvili V.I. On the stability of solitary waves in weakly dispersive media. Sov. Phys. Dokl. 15 (1970) 539-541
8. Malfliet W. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 164-165 (2004) 529-541
9. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
10. Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
11. Malfliet W., and Hereman W. The tanh method: II. Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575
12. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
13. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
14. Wazwaz A.M. The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. Appl. Math. Comput. 184 2 (2007) 1002-1014
15. Wazwaz A.M. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput. 188 (2007) 1467-1475
16. Wazwaz A.M. New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n) equations. Chaos, Solitons Fractals 13 2 (2002) 321-330
17. Matsuno Y. Bilinear Transformation Method (1984), Academic Press
18. Goktas U., and Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. J. Symbolic Comput. 11 (1999) 1-31
19. 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
20. 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
21. Hereman W., and Zhaung W. Symbolic software for soliton theory. Acta Appli. Math., Phys. Lett. A 76 (1980) 95-96
22. Hereman W., and Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simulat. 43 (1997) 13-27
23. Weiss J. On classes of integrable systems and the Painlevé property. J. Math. Phys. 25 1 (1984) 13-24
24. 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
25. Wazwaz A.M. The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation. Phys. Lett. A 366 1/2 (2007) 85-90
26. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206