Saddle-node heteroclinic orbit and exact nontraveling wave solutions for \((2 + 1)D\) KdV-Burgers equation (Q1949497)

Summary: We have undertaken the fact that the periodic solution of \((2 + 1)D\) KdV-Burgers equation does not exist. The Saddle-node heteroclinic orbit has been obtained. Using the Lie group method, we get two-\((1 + 1)\)-dimensional PDE, through symmetric reduction; and by the direct integral method, spread F-expansion method, and \((G'/G)\)-expansion method, we obtain exact nontraveling wave solutions, for the \((2 + 1)D\) KdV Burgers equation, and find out some new strange phenomenons of sympathetic vibration to evolution of nontraveling wave.