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Bifurcations of traveling wave solutions in generalized Pochhammer-Chree equation. (English) Zbl 0997.35096
Summary: Bifurcations of solitary waves and kink waves for the generalized Pochhammer-Chree equation $$u_{tt}-u_{ttxx}-\sigma(u)_{xx}=0,$$ are studied, by using the bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown. Numbers of solitary waves and kink waves are given. Under various parameter conditions, all explicit formulas of solitary wave solutions and kink wave solutions are obtained.

##### MSC:
 35Q58 Other completely integrable PDE (MSC2000) 37K50 Bifurcation problems (infinite-dimensional systems) 35C05 Solutions of PDE in closed form
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##### References:
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