The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation

Applied Mathematics and Computation

Volumn 199, Issue 1, 2008, Pages 133-138

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Hereman's method; Hirota's direct method; Multiple soliton solutions; Sawada Kotera Ito seventh order equation; Tanh coth method

Indexed keywords

INTEGRAL EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

HEREMAN'S METHOD; HIROTA'S DIRECT METHOD; MULTIPLE SOLITON SOLUTIONS; SAWADA KOTERA ITO SEVENTH ORDER EQUATION; TANH COTH METHOD;

NONLINEAR EQUATIONS;

EID: 41949134292     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.09.034     Document Type: Article

References (23)

1. Sawada K., and Kotera T. A method for finding N-soliton solutions of the KdV equation and KdV-like equation. Prog. Theor. Phys. 51 (1974) 355-1367
2. Ito M. An extension of nonlinear evolution equation of the K-dV (mK-dV) type to higher orders. J. Phys. Soc. Jpn. 49 (1980) 771-778
3. Goktas U., and Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. J. Symb. Comput. 11 (1999) 1-31
4. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
5. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
6. 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
7. Hirota R. Exact solutions of the Sine-Gordon equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1459-1463
8. 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
9. 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
10. Hereman W., and Zhaung W. Symbolic software for soliton theory, Acta Applicandae Mathematicae. Phys. Lett. A 76 (1980) 95-96
11. Hereman W., and Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simulat. 43 (1997) 13-27
12. Weiss J. On classes of integrable systems and the Painlevé property. J. Math. Phys. 25 1 (1984) 13-24
13. Goktas U., and Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. J. Symb. Comput. 11 (1999) 1-31
14. Dodd R.K., and Gibbon J.D. The prolongation structure of a higher order Korteweg-de Vries equations. Proc. Roy. Soc. Lond. A 358 (1977) 287-300
15. 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
16. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
17. Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
18. Malfliet W., and Hereman W. The tanh method: II. Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575
19. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
20. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
21. 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
22. Wazwaz A.M. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput. 188 (2007) 1467-1475
23. Wazwaz A.M. New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n) equations. Chaos Solitons Fract. 13 2 (2002) 321-330