We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the three-dimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like (antikink-like) wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.
Project supported by the National Natural Science Foundation of China (Grant No. 11701191) and Subsidized Project for Cultivating Postgraduates' Innovative Ability in Scientific Research of Huaqiao University, China.
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