一类广义KdV方程的行波解分支

Bifurcation of Traveling Wave Solutions for a Generalized KdV Equations

应用平面动力系统分支理论研究了当β>0,<0时的一类广义KdV方程ut+auβux+bu uxxx=0,证明了孤立波,扭子波与反扭子波,周期波解的存在性,并得到了所有可能的孤立波解的精确参数表示.

A class of generalized KdV equation ut＋au^βux＋bu^τuxxx, under the condition β 〉 0 and τ 〈 0 is studied by using bifurcation theorem of dynamic systems to prove the existence of solitary wave, kink and anti - kink wave, and periodic wave solutions. All possible exact parametric representations of solitary wave solutions are obtained.