Non-Lie Symmetry Group and New Exact Solutions for the Two-Dimensional KdV-Burgers Equation

By using the modified Clarkson–Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation. Under some constraint conditions, Lie point symmetry is also obtained. Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.