On positive travelling wave solutions for a general class of KdV-Burger type equation

In this paper, we establish the existence of positive traveling waves solutions for the third order differential equation ut + αuxx + βuxxx + (f (x, u(x)))x = 0, where t, x ∈ R, f is a non-negative continuous function with some properties. The result is a consequence of the characterization of the travelling wave solutions as fixed points of some functional, defined using the Green’s function associated to the linear problem, and the Krasnosel’skii fixed point theorem on cone expansion and compression of norm type.