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

TL;DR

This paper completes the classification of Q-conditional symmetries for reaction-diffusion-convection equations with arbitrary nonlinearities, highlighting limitations in extending previous results to new nonlinear cases.

Contribution

It provides a comprehensive description of Q-conditional symmetries for these equations and clarifies the boundaries of previous findings regarding nonlinearities.

Findings

Complete description of Q-conditional symmetries achieved.

Previous results cannot be extended to new nonlinearities.

Clarification of limitations in symmetry extensions.

Abstract

A complete description of $Q$-conditional symmetries of reaction-diffusion-convection equation with arbitrary power nonlinearities is finished. It is shown that the results obtained in the first and second parts of this work (see arXiv:math-ph/0612078 and arXiv:0706.0814) cannot be extended on new power nonlinearities arising in the diffusion and convection coefficients.