耦合KdV型方程有界行波解的存在性及其显式表达式

On Existence and Explicit Expression of Bounding Traveling Wave Solutions to Coupled KdV-Type Equation

利用平面动力系统理论对非线性耦合KdV型方程的行波解进行定性分析,给出耦合方程所对应的平面动力系统在不同参数条件下的相图和有界行波解存在的条件.得出耦合方程只可能存在钟状孤波解和周期解,并利用改进的(G′/G)方法求出了方程4个有界行波解的显式表达式.

Applying the theory of planar dynamical systems,we have carried out qualitative analysis for traveling wave solutions of the coupled KdV-type equation.We have obtained some phase portraits for the planar dynamical systems associated with them under different parameters conditions.Furthermore,we present the existence of bounded traveling wave solutions for the coupled KdV-type equation,and that it exists only the bell solitary wave solutions and periodic solutions.Finally,we have investigated that the explicit expression of four bounding traveling wave solutions by the improved（G′/G）-expansion method.