Bifurcations of travelling wave solutions for modified nonlinear dispersive phi-four equation

Applied Mathematics and Computation

Volumn 217, Issue 4, 2010, Pages 1584-1597

  Zhou, Hongxian ^a   Shen, Jianwei ^a  

^a XUCHANG UNIVERSITY   (China)

Author keywords

Bifurcation theory; Compactons; Periodic wave; Phi four equation; Smoothness of waves; Solitary wave

Indexed keywords

BIFURCATION THEORY; COMPACTONS; PERIODIC WAVES; PHI-FOUR EQUATION; SMOOTHNESS OF WAVES; SOLITARY WAVE;

BIFURCATION (MATHEMATICS); DYNAMICAL SYSTEMS; MECHANICAL WAVES; SOLITONS;

NONLINEAR EQUATIONS;

EID: 77957286776     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.07.001     Document Type: Article

References (21)

1. E. Fan, and H. Zhang New exact solutions for a system of coupled KdV equation Phys. Lett. A 245 1998 389 392 (Pubitemid 128398883)
2. E. Fan, and H. Zhang A note on the homogeneous balance method Phys. Lett. A 246 1998 403 406 (Pubitemid 128400793)
3. E. Fan Extended tanh-function method and its applications to nonlinear equations Phys. Lett. A 212 2000 277 284 (Pubitemid 32001663)
4. Y. Chen, B. Li, and H. Zhang New exact solutions for modified nonlinear dispersive equations mK(m, n) in higher dimensional spaces Math. Comput. Simul. 64 2004 549 559
5. L. Tian, and S. Yu Nonsymmetrical compacton and multi-compacton of nonlinear intensity Klein-Gordon equation Chaos Solitons Fract. 29 2006 282 293 (Pubitemid 43152194)
6. A.M. Wazwaz Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation Appl. Math. Comput. 134 2003 487 500
7. A.M. Wazwaz Compactons in a class of nonlinear dispersive equations Math. Comput. Modell. 37 3-4 2003 333 341 (Pubitemid 36257630)
8. A.M. Wazwaz Generalized forms of the phi-four equation with compactons, solitons and periodic solutions Math. Comput. Simul. 69 2005 580 588 (Pubitemid 41084735)
9. I. Dag, B. Saka, and D. Irk Galerkin method for the numerical solution of the RLW equation using quintic B-splines J. Comput. Appl. Math. 190 2006 532 547 (Pubitemid 43189968)
10. F.M. Allan, and K. Al-Khaled An approximation of the analytic solution of the shock wave equation J. Comput. Appl. Math. 192 2006 301 309
11. Y. Lou Bifurcation of travelling wave solutions in generalized phi-four equation Appl. Math. Comput. 190 2007 517 525 (Pubitemid 46856682)
12. S.N. Chow, and J.K. Hale Method of Bifurcation Theory 1981 Springer-Verlag New York
13. J. Guckenheimer, and P.J. Holmes Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields 1983 Springer-Verlag New York
14. L. Perko Differential Equations and Dynamical Systems 1991 Springer-Verlag New York
15. H. Dai Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods Wave Motion 28 4 1998 367 381 (Pubitemid 128348970)
16. J. Li, and Z. Liu Smooth and non-smooth traveling waves in a nonlinearly dispersive equation Appl. Math. Modell. 25 2000 41 56 (Pubitemid 32086784)
17. J. Li, and Z. Liu Travelling waves for a class of nonlinear dispersive equations Chin. Ann. Math. Ser. B 23 3 2002 397 418
18. J. Li, J. Wu, and H. Zhu Travelling wave solutions for an integrable higher order KDV type equations Int. J. Bifurcat. Chaos 16 8 2006 2235 2260 (Pubitemid 44671745)
19. J. Shen, J. Li, and W. Xu Bifurcations of travelling wave solutions in a model of the hydrogen-bonded systems Appl. Math. Comput. 171 2005 242 271 (Pubitemid 41737300)
20. H. Dai, and Y. Huo Solitary shock waves and other travelling waves in a general compressible hyperelastic rod Proc. Roy. Soc. Lond. A 456 2000 331 363
21. J. Grasman Asymptotic Methods for Relaxation Oscillations and Applications 1987 Springer-Verlag New York