A Class Of Generalized Coupled Hirota,-satsuma System Of The Kdv System Traveling Wave Solutions

This paper includes three parts. In the first part, We change the generalized coupled Hirota-Satsuma KdV equations into a planar Hamiltonian system (1.5b) by assuming a two-dimensional surface and obtain the parameter conditions by comparing the coefficients;In the second part, we present the bifurcation sets, bifurcation curves and phase portraits of (1.5b);In the third part, fourteen types explicit formulas of solitary wave solutions, anti-kink wave solutions and periodic wave solutions are obtained.