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

In this paper, we consider compound KdV-type and KdV–Burgers-type equations with nonlinear terms of any order. The explicit exact solitary-wave solutions for the equations are obtained by means of proper transformation, which degrades the order of nonlinear terms, and an undetermined coefficient method. A solitary-wave solution with negative velocity for the generalized KdV–Burgers equation ut+upux−αuxx+uxxx=0 is found.