Potential equivalence transformations for nonlinear diffusion-convection equations

TL;DR

This paper classifies potential symmetries of nonlinear diffusion-convection equations, demonstrates their connection to point symmetries via potential equivalence transformations, and explores their impact on solutions.

Contribution

It provides a comprehensive classification of potential symmetries for a class of nonlinear diffusion-convection equations and links them to point symmetries through PETs.

Findings

All potential symmetries are classified.

Known non-local transformations are identified as PETs.

PETs act on solutions of fast diffusion equations.

Abstract

Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are classified and a theorem on connection of them with point ones via PETs is also proved. It is shown that the known non-local transformations between equations under consideration are nothing but PETs. Action of PETs on sets of exact solutions of a fast diffusion equation is investigated.