The extended tanh method for abundant solitary wave solutions of nonlinear wave equations

Applied Mathematics and Computation

Volumn 187, Issue 2, 2007, Pages 1131-1142

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Dispersion; Dissipation; Extended tanh method; Kinks; Nonlinear wave equations; Solitons

Indexed keywords

DISPERSION (WAVES); NONLINEAR EQUATIONS; NUMERICAL METHODS; SOLITONS;

DISSIPATION; EXTENDED TANH METHOD; KINKS; NONLINEAR WAVE EQUATIONS;

WAVE EQUATIONS;

EID: 34247279667     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.09.013     Document Type: Article

References (22)

1. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
2. Malfliet W., and Hereman W. The tanh method. I: Exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54 (1996) 563-568
3. Malfliet W., and Hereman W. The tanh method. II: Perturbation technique for conservative systems. Phys. Scr. 54 (1996) 569-575
4. Hereman W., and Malfliet W. The tanh method: a tool to solve nonlinear partial differential equations with symbolic software. Proceedings 9th World Multi-Conference on Systemics (2005), Cybernetics and Informatics, Orlando, FL 165-168
5. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
6. Wazwaz A.M. The tanh method: exact solutions of the Sine-Gordon and the Sinh-Gordon equations. Appl. Math. Comput. 49 (2005) 565-574
7. Wazwaz A.M. The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Comm. Nonlinear Sci. Numer. Simul. 11 2 (2006) 148-160
8. Wazwaz A.M. The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Appl. Math. Comput. 167 2 (2005) 1179-1195
9. Wazwaz A.M. The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos, Solitons Fractals 25 1 (2005) 55-63
10. Wazwaz A.M. The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations. Appl. Math. Comput. 169 (2005) 321-338
11. Wazwaz A.M. Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations. Appl. Math. Comput. 169 (2005) 639-656
12. A.M. Wazwaz, The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.07.002.
13. A.M. Wazwaz, New solitary wave solutions to the modified forms of Degasperis-Procesi and Camass-Holm equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.07.092.
14. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
15. Wazwaz A.M. Solitary wave solutions for modified forms of the Degasperis-Procesi and Camassa-Holm and equations. Phys. Lett. A 352 (2006) 500-504
16. Wazwaz A.M. A study on nonlinear dispersive partial differential equations of compact and noncompact solutions. Appl. Math. Comput. 135 2-3 (2003) 399-409
17. Wazwaz A.M. A construction of compact and noncompact solutions of nonlinear dispersive equations of even order. Appl. Math. Comput. 135 2-3 (2003) 324-411
18. Wazwaz A.M. Compactons in a class of nonlinear dispersive equations. Math. Comput. Modell. 37 3-4 (2003) 333-341
19. Wazwaz A.M. Variants of the two-dimensional Boussinesq equations with compactons, solitons and periodic solutions. Comput. Math. Appl. 49 (2005) 295-301
20. Wazwaz A.M. New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations. Chaos, Solitons Compact. 22 1 (2004) 249-260
21. Wazwaz A.M. Special types of the nonlinear dispersive Zakharov-Kuznetsov equation with compactons, solitons and periodic solutions. Int. J. Comput. Math. 81 9 (2004) 1107-1119
22. Wazwaz A.M. A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompact solutions. Appl. Math. Comput. 165 (2005) 485-501