Differential constraints and exact solutions of nonlinear diffusion equations

TL;DR

This paper introduces a method using differential constraints and linear determining equations to find explicit solutions for nonlinear diffusion equations, extending classical symmetry approaches.

Contribution

It presents a novel approach that generalizes classical Lie symmetry methods through the use of parameterized linear determining equations for solving nonlinear diffusion equations.

Findings

Explicit solutions for nonlinear diffusion equations are obtained.

The method extends classical symmetry techniques.

The approach simplifies finding solutions to complex nonlinear PDEs.

Abstract

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries.