Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation

Abstract

For a generalized KdV-Burgers-Kuramoto equation we have studied conservation laws by using the multiplier method, and investigated its first-level and second level potential systems. Furthermore, the Lie point symmetries of the equation and the Lie point symmetries associated with the conserved vectors are determined. We obtain travellingwave reductions depending on the form of an arbitrary function. We present some explicit solutions: soliton solutions, kinks and antikinks.