Application of Lie group analysis to functional differential equations

TL;DR

This paper extends classical symmetry analysis methods to functional differential equations, enabling new analytical approaches for complex systems in physics and fluid dynamics.

Contribution

It introduces a novel extension of Lie group analysis to functional derivatives, broadening the scope of symmetry methods for differential equations.

Findings

Extended symmetry analysis to functional derivatives.

Applied method to continuum heat equation.

Potential applications in physics and fluid dynamics.

Abstract

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional derivatives we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example the procedure is applied to the continuum limit of the heat equation. The method can further lead to significant applications in statistical physics and fluid dynamics.