In this talk, we consider the KdV-Burgers-Kuramoto equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. We convert the problem into an equivalent 3D-dimensional system and analyze its local dynamical behaviors. By means of the Lie symmetry reduction method and the Preller-Singer procedure, we show that there exist nontrivial bounded wave solutions under certain parametric conditions. Numerical simulations of wave phenomena are illustrated, which provide us rich dynamical information and are in agreement with our theoretical analysis.

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