Bifurcations of Travelling Wave Solutions for a Coupled Nonlinear Wave System
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摘要: 利用动力系统的Hopf分支理论来研究耦合非线性波方程周期行波解的存在性和稳定性.应用行波法把一类耦合非线性波方程转换为三维动力系统来研究,从而给在不同的参数条件下给出了周期解存在和稳定性的充分条件.Abstract: By using the bifurcation theory of dynamical systems to the coupled nonlinear wave equations, the existence and stability of periodic wave solutions by Hopf bifurcations are obtained. Theory of travelling wave was applied to transforma kind of the coupled nolinear wave equations into three- dimension dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence and stability of the above so lutions are given.
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Key words:
- travelling wave solution /
- Hopf bifurcation /
- nonlinear wave equation
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[1] 房少梅,郭柏灵.一类广义耦合的非线性波动方程组时间周期解的存在性[J].应用数学和力学,2003,24(6):595—604. [2] Chow S N,Hale J K.Method of Bifurcation Theory[M].New York:Springer-Verlag,1981. [3] Debnath L.Nonlinear Partial Differential Equations for Scientists and Engineers[M].Boston:Birkhauser,1997. [4] Guckenheimer J,Holmes P J.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag,1983. [5] 李继彬,冯贝叶.稳定性、分支与混沌[M].昆明:云南科技出版社,1995. [6] Hassard B D,Wan Y H.Bifurcation formulae derived from center manifold theory[J].Journal of Mathematical Analysis and Applications,1978,63(2):297—312. doi: 10.1016/0022-247X(78)90120-8 [7] Hassard B D,Kazarinoff N D,Wan Y H.Theory and Applications of Hopf Bifurcation[M].London:Cambridge University Press,1981.
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