New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

TL;DR

This paper identifies new conditional symmetries for nonlinear reaction-diffusion-convection equations and uses them to construct exact solutions, including novel solutions relevant to practical applications.

Contribution

It extends previous work by deriving comprehensive Q-conditional symmetries and applying them to find new exact solutions of RDC equations.

Findings

New exact solutions of nonlinear RDC equations are obtained.

Symmetries enable the construction of solutions relevant to applications.

Previous results are special cases of the new symmetry framework.

Abstract

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found.