Lie Group Classification for a Class of Compound KdV–Burgers Equations with Time-Dependent Coefficients

Abstract

We derive the Lie group classification for a general class of KdV–Burgers equations, where the coefficients are functions of time. We demonstrate how important is the use of equivalence transformations prior the group classification. These transformations have a great effect for the simplification of the symmetry analysis. The derived Lie symmetries are employed to transform problems with a partial differential equation along with certain conditions to initial value problems with a corresponding ordinary differential equation. A discussion for more general classes of related equations is given.