Abstract
By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jaulent M, Miodek I. Nonlinear evolution equations associated with energy dependent Schrodinger potentials[J]. Lett Math Phys, 1976, 1(3):243–250.
Fan Engui. Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics[J]. Chaos, Solitons and Fractals, 2003, 16(5):819–839.
Chow S N, Hale J K. Method of bifurcation theory[M]. New York: Springer-Verlag, 1981.
Guckenheimer J, Holmes P J. Nonlinear oscillations, dynamical systems and bifurcations of vector fields[M]. New York: Springer-Verlag, 1983.
Li Jibin. Solitary and periodic travelling wave solutions in Klein-Gordon-Schrodinger equation[J]. Journal of Yunnan University, 2003, 25(3):176–180.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contributed by LI Ji-bin
Rights and permissions
About this article
Cite this article
Feng, Dh., Li, Jb. Bifurcations of travelling wave solutions for Jaulent-Miodek equations. Appl Math Mech 28, 999–1005 (2007). https://doi.org/10.1007/s10483-007-0802-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-007-0802-1