一类非线性偏微分方程行波解的分支

Bifurcations of Travelling Wave Solutions for A Class of Nonlinear Partial Differential Equations

利用动力系统理论、分支理论和直接方法研究了一类非线性偏微分方程（NPDEs），证明了此类方程存在光滑孤立波解，扭结波解和不可数无穷多光滑周期波解，求出了该方程用参数表示的显式精确行波解。并在不同的参数条件下，给出了上述光滑孤立波解，扭结波解和不可数无穷多光滑周期波解存在的各类充分条件。

The theory of dynamical systems and the theory of bifurcation and the direct method were used to investigate a class of nonlinear partial differential equations(NPDEs).The existence of smooth solitary wave solutions,kink wave solution and uncountably infinite many smooth periodic wave solutions is proved.It obtaines some exact explicit parametric representations of travelling wave solutions of the equations.Under different parametric conditions,various sufficient conditions are given to guarantee the existence of the above solutions.