Abstract
By using the bifurcation method of dynamical systems and numerical simulation approach of differential equations, we investigate generalized KdV equation \(u_t=u^{2}u_{x}-u^{2}u_{xxx}-4uu_xu_{xx}-(u_x)^3\). Two types of bounded traveling wave solutions are found, that is, the kink-like wave and compacton-like wave solutions. The planar graphs of these solutions are simulated by using software Mathematica; meanwhile, some interesting phenomena are revealed, that is, under some conditions, the periodic wave can become the kink-like wave and compacton-like wave, respectively, and the solitary wave can become the kink-like wave. The exact kink-like wave and compacton-like wave solutions with implicit or parameter expressions are given.
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