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 transform a kind of coupled nonlinear wave equations into three-dimension dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence and stability of the above solutions are given.
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References
Fang Shaomei, Guo Boling. Existence of time periodic solutions for a damped generalized coupled nonlinear wave equations[J].Applied Mathematics and Mechanics (English Edition), 2003,24(6): 673–683.
Chow S N, Hale J K.Method of Bifurcation Theory[M] Springer-Verlag, New York, 1981.
Debnath L.Nonlinear Partial Differential Equations for Scientists and Engineers[M]. Birkhauser, Boston, 1997.
Guckenheimer J, Holmes P J.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M]. Springer-Verlag, New York, 1983.
Li Jibin, Feng Beiye.Stability, Bifurcations and Chaos[M]. Yunnan Scientific Press, Kunming, 1995 (in Chinese).
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.
Hassard B D, Kazarinoff N D, Wan Y H.Theory and Applications of Hopf Bifurcation[M]. Cambridge University Press, London, 1981.
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Ji-xiang, Z., Ji-bin, L. Bifurcations of travelling wave solutions for a coupled nonlinear wave system. Appl Math Mech 26, 838–847 (2005). https://doi.org/10.1007/BF02464232
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DOI: https://doi.org/10.1007/BF02464232