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

TL;DR

This paper provides a comprehensive analysis of Q-conditional symmetries for specific reaction-diffusion-convection equations, expanding the known solutions and demonstrating that previous results are special cases of the new findings.

Contribution

It introduces a complete description of Q-conditional symmetries for reaction-diffusion-convection equations with power diffusivities, generalizing prior results.

Findings

All known solutions for reaction-diffusion equations with power diffusivities are special cases of the new results.

The paper derives a complete set of Q-conditional symmetries for the studied equations.

New exact solutions are obtained from the symmetry analysis.

Abstract

A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained here but not vise versa.