Abstract

In this paper, bounded traveling waves of a generalized Burgers–Fisher equation are investigated. By studying some complicated local and nonlocal bifurcations such as the Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation and Poincaré bifurcation of the corresponding traveling wave system, we obtain sufficient conditions to guarantee the existence of different kinds of bounded traveling waves, including solitary waves, kink waves and periodic waves. Further, we discuss the existence of various oscillatory bounded traveling waves.

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