The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations

Applied Mathematics and Computation

Volumn 188, Issue 2, 2007, Pages 1467-1475

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Kinks; Nonlinear parabolic equations; Solitons; The tanh coth method

Indexed keywords

NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SOLITONS;

FISHER EQUATION; KINKS; NONLINEAR PARABOLIC EQUATIONS; TANH-COTH METHOD;

NONLINEAR EQUATIONS;

EID: 34248229664     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.013     Document Type: Article

References (24)

1. Polyanin A.D., and Zaitsev V.F. Handbook of Nonlinear Partial Differential Equations (2004), Chapman & Hall/CRC
2. Voigt A. Asymptotic behavior of solutions to the Allen-Cahn equation in spherically symmetric domains. Caesar Preprints (2001) 1-8
3. Allen S.M., and Cahn J.W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1085-1095
4. Rosu H.C., and Cornejo-Pérez O. Supersymmetric pairing of kinks for polynomial nonlinearities. Phys. Rev. E 71 (2005) 1-13
5. Wazwaz A.M., and Gorguis A. An analytic study of Fisher's equation by using Adomian decomposition method. Appl. Math. Comput. 154 3 (2004) 609-620
6. Hirota R. Direct Methods in Soliton Theory (1980), Springer, Berlin
7. Ablowitz M., and Segur H. Solitons and the Inverse Scattering Transform (1981), SIAM, Philadelphia
8. Lax P.D. Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 62 (1968) 467-490
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. Goktas U., and Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. J. Symbolic Comput. 24 (1997) 591-621
13. Baldwin D., Goktas U., Hereman W., Hong L., Martino R.S., and Miller J.C. Symbolic computation of exact solutions in hyperbolic and elliptic functions for nonlinear PDEs. J. Symbolic Comput. 37 (2004) 669-705
14. Hereman W., and Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simul. 43 (1997) 13-27
15. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
16. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
17. Wazwaz A.M. The tanh method: exact solutions of the Sine-Gordon and the Sinh-Gordon equations. Appl. Math. Comput. 49 (2005) 565-574
18. Wazwaz A.M. Variants of the two-dimensional Boussinesq equations with compactons, solitons and periodic solutions. Comput. Math. Appl. 49 (2005) 295-301
19. Wazwaz A.M. The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Commun. Nonlinear Sci. Numer. Simul. 112 (2006) 148-160
20. Wazwaz A.M. New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations. Chaos, Solitons Compactons 22 1 (2004) 249-260
21. Wazwaz A.M. The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equation. Appl. Math. Comput. 169 (2005) 321-338
22. A.M. Wazwaz, New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.07.092.
23. 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.
24. A.M. Wazwaz, The extended tanh method for abundant solitary wave solutions of nonlinear wave equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.09.013.