The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations

Journal of Computational and Applied Mathematics

Volumn 164-165, Issue , 2004, Pages 529-541

  Malfliet, W ^a  

^a UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Nonlinear travelling waves

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; DIFFUSION; MATHEMATICAL MODELS; PROBLEM SOLVING;

MATHEMATICAL BIOLOGY; NONLINEAR WAVES;

NONLINEAR SYSTEMS;

MATHEMATICAL MODELING; WAVE;

EID: 1442264988     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00645-9     Document Type: Article

References (25)

1. Ablowitz M. Kaup D. Newell A. Segur H. The inverse scattering transform-Fourier analysis for nonlinear problems Stud. Appl. Math. 53 1974 249-315
2. Baldwin D. Göktas Ü. Hereman W., et-al. Symbolic computation of tanh and sech solutions of NL PDEs and differential-difference equations J. Symbolic. Comput. 11 2000 1-12
3. R. Conte (Ed.), The Painlevé Property, Springer, Berlin, 1999.
4. Davidson R. Methods in Nonlinear Plasma Theory 1972 Academic Press New York
5. Fan E.G. Hong Y.C. Double periodic solutions with Jacobi elliptic functions for two generalized Hirota-Satsuma coupled KdV system Phys. Lett. A 292 2002 335-340
6. Gao Y.T. Tian B. Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations to nonlinear equations of mathematical physics Comput. Phys. Commun. 133 2-3 2001 158-164
7. Gray P. Scott S. Chemical Oscillations and Instabilities 1990 Clarendon Press Oxford
8. Grindrod P. Patterns and Waves 1991 Clarendon Press Oxford
9. Hirota R. Direct method of finding exact solutions of nonlinear evolution equations Bullough R. Caudrey P. Backlund Transformations 1980 1157-1175 Springer Berlin
10. Horsthemke W. Fisher waves in reaction random walks Phys. Lett. A 263 1999 285-292
11. Ichikawa Y.H. Watanabe S. Solitons and envelope solitons in collissionless plasmas J. Phys. (Paris) 38 1977 C6-C15
12. Johnston C.R. Epstein M. On the exact amplitude, speed and shape of ion-acoustic waves Phys. Plasmas 7 2000 906-910
13. Malfliet W. Series solution of nonlinear coupled reaction-diffusion equations J. Phys. A: Math. Gen. 24 1991 5499-5503
14. Malfliet W. Solitary wave solutions of nonlinear wave equations Amer. J. Phys. 60 1992 650-654
15. Malfliet W. Hereman W. The Tanh method: I Exact solutions of nonlinear evolution and wave equations Phys. Scripta 54 1996 563-568
16. Malfliet W. Hereman W. The Tanh method: II Perturbation technique for conservative systems Phys. Scripta 54 1996 569-575
17. Malfliet W. Wieers E. The theory of nonlinear ion-acoustic waves revisited J. Plasma Phys. 56 1996 441-450
18. J. Merkin, D. Needham, Reaction-diffusion waves in simple isothermal chemical systems, in: J. Engelbrecht (Ed.), Nonlinear Waves in Active Media, Springer, Berlin, 1989, pp. 232-242.
19. Murray J. Mathematical Biology 1989 Springer Berlin
20. Parkes E. Exact solutions to the two-dimensional Korteweg-De Vries-Burgers equation J. Phys. A: Math. Gen. 27 1994 L497-L501
21. Toda M. Studies of a Nonlinear Lattice 1981 Springer Berlin
22. Verbist G. Weaire D. A soluble model for foam drainage Europhys. Lett. 26 1994 631-639
23. Weissert T.P. The Genesis of Simulation in Dynamics (Pursuing the FPU Problem) 1997 Springer New York
24. Whitham G. Linear and Nonlinear Waves 1974 Wiley New York
25. Zabusky N. Solitons and energy transport in nonlinear lattices Comput. Phys. Commun. 5 1979 1-10