On travelling wave solutions of some nonlinear evolution equations

International Journal of Computer Mathematics

Volumn 81, Issue 2, 2004, Pages 191-202

  Inc, M ^a   Evans, D J ^b  

^a FIRAT UNIVERSITY   (Turkey)

^b NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

Author keywords

Hyperbolic function method; Nonlinear evolution equation; Symbolic computation; Travelling wave solution

Indexed keywords

FUNCTIONS; WAVE EQUATIONS;

HYPERBOLIC FUNCTION METHOD; NONLINEAR EVOLUATION EQUATION; SYMBOLIC COMPUTATION; TRAVELLING WAVE SOLUTION;

NONLINEAR EQUATIONS;

EID: 14744289073     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160310001603307     Document Type: Article

References (22)

1. M. Iwao and R. Hirota, Soliton solutions of a coupled derivative modified KdV equations, J. Phys. Soc. Japan, 69 (2000) 59.
2. M. J. Ablowitz and P. A. Clarkson, Solitons: Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge (1991).
3. F. Cariello and M. Tabor, Painlevé expansions for nonintegrable evolution equations, Physica D, 39 (1989) 77.
4. W. Hereman and M. Takaoka, Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, J. Phys. A: Math. Gen., 23 (1990) 4805.
5. X. Zhao and D. Teng, A new note on a homogeneous balance method, Phys. Lett. A, 297 (2002) 59.
6. E. G. Fan, Darboux transformation and soliton-like solutions for the Gerdijikov-Ivanov equation, J. Phys. A: Math. Gen., 33 (2000) 6925.
7. P. J. Olver, Applications of Lie Groups to Differential Equations, New York, Springer (1993).
8. X. Feng, Exploratory approach to explicit solution of nonlinear evolution equations, Intern. J. Theor. Phys., 39 (2000) 207.
9. E. G. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277 (2000) 212.
10. E. G. Fan, Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation, Phys. Lett. A, 282 (2001) 18.
11. E. G. Fan and Y. C. Hon, Generalized tanh-function method extended to special types of nonlinear equations, Z. Naturforsch, 57a (2002) 692.
12. E. G. Fan, Travelling wave solutions for two generalized Hirota-Satsuma KdV systems, Z. Naturforsch, 56a (2001) 312.
13. S. A. Elwakil, S. K. El-labany, M. A. Zahran and R. Sabry, Two new applications of the modified extended tanh-function method, Z. Naturforsch, 58a (2003) 39.
14. Z. Yan, A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations, Chaos, Solitons and Fractals, 16 (2003) 291.
15. E. G. Fan, A new algebraic method for finding the line soliton solutions and doubly periodic wave solution to a two-dimensional perturbed KdV equation, Chaos, Solitons and Fractals, 15 (2003) 567.
16. E. G. Fan, Unformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics, Chaos, Solitons and Fractals, 16 (2003) 819.
17. E. J. Parkers, B. R. Duffy and P. C. Abbott, The Jacobi elliptic function method for finding periodic-wave solutions to nonlinear evolution equations, Phys. Lett. A, 295 (2002) 280.
18. E. G. Fan and J. Zhang, Applications of Jacobi elliptic function method to special type nonlinear equations, Phys. Lett. A, 305 (2002) 383.
19. C. Bai, Exact solutions for nonlinear PDE: a new approach, Phys. Lett. A, 288 (2001) 191.
20. F. Xie, Z. Yan and H. Q. Zhang, Explicit and exact travelling wave solutions of Whitham-Broer-Kaup shallow water equations, Phys. Lett. A, 285 (2001) 76.
21. W. Wu, Algorithms and Computation, Springer, Berlin (1994).
22. H. Chen and H. Q. Zhang, Improved Jacobi elliptic function method and its applications, Chaos, Solitons and Fractals, 15 (2003) 585.