The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations

Applied Mathematics and Computation

Volumn 169, Issue 1, 2005, Pages 321-338

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Burgers Fisher equation; KdV equation; Nonlinear heat conduction; The tanh method; Travelling wave solutions

Indexed keywords

HEAT CONDUCTION;

BURGERS-FISHER EQUATION; KDV METHOD; NONLINEAR HEAT CONDUCTION; THE TANH METHOD; TRAVELING WAVE EQUATION;

NONLINEAR EQUATIONS;

EID: 27144553113     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.09.054     Document Type: Article

References (20)

1. E. Fan Extended tanh-function method and its applications to nonlinear equations Phys. Lett. A 277 2000 212 218
2. M. Wadati Introduction to solitons Pramana: J. Phys. 57 5-6 2001 841 847
3. M. Wadati The exact solution of the modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 32 1972 1681 1687
4. Y.S. Kivshar, and D.E. Pelinovsky Self-focusing and transverse instabilities of solitary waves Phys. Rep. 331 2000 117 195
5. W. Hereman, and M. Takaoka Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA J. Phys. A 23 1990 4805 4822
6. W. Malfliet Solitary wave solutions of nonlinear wave equations Am. J. Phys. 60 7 1992 650 654
7. W. Malfliet The tanh method: I. Exact solutions of nonlinear evolution and wave equations Phys. Scr. 54 1996 563 568
8. W. Malfliet The tanh method: II. Perturbation technique for conservative systems Phys. Scr. 54 1996 569 575
9. A.M. Wazwaz The tanh method for travelling wave solutions of nonlinear equations Appl. Math. Comput. 154 3 2004 713 723
10. A.M. Wazwaz Partial Differential Equations: Methods and Applications 2002 Balkema Publishers The Netherlands
11. 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
12. 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
13. 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
14. 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
15. 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
16. A.M. Wazwaz A construction of compact and noncompact solutions of nonlinear dispersive equations of even order Appl. Math. Comput. 135 2-3 2003 324 411
17. A.M. Wazwaz Compactons in a class of nonlinear dispersive equations Math. Comput. Model. 37 3/4 2003 333 341
18. A.M. Wazwaz Distinct variants of the KdV equation with compact and noncompact structures Appl. Math. Comput. 150 2004 365 377
19. A.M. Wazwaz Variants of the generalized KdV equation with compact and noncompact structures Comput. Math. Appl. 47 2004 583 591
20. A.M. Wazwaz New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations Chaos, Solitons Fract. 22 2004 249 260