Abstract
In this paper, the bifurcations of solitary, kink, anti-kink, and periodic waves for the generalized coupled Hirota–Satsuma KdV system is studied by using the bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown, under given parameter conditions, explicit formulas of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions are obtained.
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