Explicit exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order

In this paper, we improved a method presented previously (Phys. Lett. A 285 (2001) 355) by means of a proper transformation. Applying the improved method, we consider the generalized compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions, are obtained.