The application of bifurcation method to a higher-order KdV equation ✩

Bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the higher-order KdV equation ut + aunux +uxxx = 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.  2002 Elsevier Science (USA). All rights reserved.