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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 $n\ge 1$ and $a\in\bbfR$. 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.

35Q53KdV-like (Korteweg-de Vries) equations
37K50Bifurcation problems (infinite-dimensional systems)
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
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