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The application of bifurcation method to a higher-order KdV equation. (English) Zbl 1012.35076
Summary: Bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the higher-order KdV equation $u_t+au^nu_x +u_{xxx}=0,$ where $$n\geq 1$$ and $$a\in\mathbb{R}$$. Numbers of solitary waves are given for each parameter condition. Under some parameter conditions, explicit solitary wave solutions are obtained. Specially, some new solitary wave solutions are found for the KdV or MKDV equation.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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##### References:
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