The main goal of this paper is to focus on travelling wave solutions of equations
where , , , and are real constants, and is a positive number. The authors transform the so-called Burgers-KdV-type equation (2) to a two-dimensional autonomous system and apply the qualitative theory of planar dynamical systems to analyze the resultant system for its solitary waves. A qualitative analysis to the equation (2) is presented, which indicates that under given parametric conditions, the equation (2) has neither nontrivial bell-profile solitary waves, nor periodic waves. The authors show that a solitary wave solution is obtained by using the first-integral method.