(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the D(m,n) equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the D(m,n) system including all the solutions which have been found from the references [4, 14, 17].