The tanh method: Exact solutions of the sine-Gordon and the sinh-Gordon equations

Applied Mathematics and Computation

Volumn 167, Issue 2, 2005, Pages 1196-1210

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Sine Gordon equation; Sinh Gordon equation; Tanh method; Traveling wave solutions

Indexed keywords

ALGEBRA; MATHEMATICAL MODELS;

SINE-GORDON EQUATION; SINH-GORDON EQUATION; THE TANH METHOD; TRAVELING WAVE SOLUTIONS;

LINEAR EQUATIONS;

EID: 25144450080     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.08.005     Document Type: Article

References (26)

1. J.K. Perring, and T.H. Skyrme A model unified field equation Nucl. Phys. 31 1962 550 555
2. M.J. Ablowitz, B.M. Herbst, and C. Schober On the numerical solution of the sine-Gordon equation J. Comput. Phys. 126 1996 299 314
3. W. Malfliet Solitary wave solutions of nonlinear wave equations Am. J. Phys. 60 7 1992 650 654
4. W. Malfliet, The tanh method. I. Exact solutions of nonlinear evolution and wave equations, Phys. Scr. 54, 563-568.
5. W. Malfliet, The tanh method. II. Perturbation technique for conservative systems, Phys. Scr. 54, 569-575.
6. A.H. Khater, W. Malfliet, D.K. Callebaut, and E.S. Kamel The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations Chaos, Solitons Fract. 14 2002 513 522
7. E.J. Parkes, and B.R. Duffy An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations Comput. Phys. Commun. 98 1996 288 300
8. K. Glasner Nonlinear preconditioning for diffuse interfaces J. Comput. Phys. 174 2001 695 711
9. T. Kawahara, and M. Tanaka Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation Phys. Lett. A 97 8 1983 311 314
10. R. Conte, and M. Mussette Link between solitary waves and projective Riccati equations J. Phys.: Math. Gen. 25 1992 5609 5623
11. L. Huibin, and W. Kelin Exact solutions for two nonlinear equations: I J. Phys. A: Math. Gen. 23 1990 3923 3928
12. M. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A, 213, 279-287.
13. W. Ma Travelling wave solutions to a seventh order generalized KdV equation Phys. Lett. A 180 1993 221 224
14. G.W. Wei Discrete singular convolution for the sine-Gordon equation Physica D 137 2000 247 259
15. E. Fan, and Y.C. Hon Generalized tanh method extended to special types of nonlinear equations Z. Naturforsch. A 57a 2002 692 700
16. A.M. Wazwaz Partial Differential Equations: Methods and Applications 2002 Balkema Publishers The Netherlands
17. A.M. Wazwaz New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations Chaos, Solitons Fract. 13 2 2002 321 330
18. A.M. Wazwaz Exact specific solutions with solitary patterns for the nonlinear dispersive K(m, n) equations Chaos, Solitons Fract. 13 1 2001 161 170
19. A.M. Wazwaz General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 213 227
20. A.M. Wazwaz General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 229 244
21. A.M. Wazwaz A study of nonlinear dispersive equations with solitary-wave solutions having compact support Math. Comput. Simul. 56 2001 269 276
22. A.M. Wazwaz Compactons dispersive structures for variants of the K(n, n) and the KP equations Chaos, Solitons Fract. 13 5 2002 1053 1062
23. A.M. Wazwaz Compactons and solitary patterns structures for variants of the KdV and the KP equations Appl. Math. Comput. 139 1 2003 37 54
24. A.M. Wazwaz Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method Chaos, Solitons Fract. 12 8 2001 1549 1556
25. A.M. Wazwaz A computational approach to soliton solutions of the Kadomtsev-Petviashili equation Appl. Math. Comput. 123 2 2001 205 217
26. A.M. Wazwaz The tanh method for travelling wave solutions of nonlinear equations Appl. Math. Comput. 154 3 2004 713 723