Abstract
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⩾1 and a∈ 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 KdV or MKdV equation.
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