Abstract
<abstract> This paper studies traveling wave solutions of three modified Camassa-Holm equations posed by Anco and Recio in 2019. The corresponding traveling system is a singular system of second class. The bifurcations of traveling wave solutions in the parameter space are investigated from a dynamical systems theoretical point of view. The existence of solitary wave solution, periodic wave solution and so-called $M$-shape-solution are proved. </abstract>
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