Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation

TL;DR

This paper develops a framework for approximate Q-conditional symmetries of PDEs, applying it to a hyperbolic reaction-diffusion-convection equation to find explicit approximate solutions.

Contribution

It introduces a consistent approach to approximate Q-conditional symmetries aligned with perturbation theory, applied to a specific hyperbolic PDE.

Findings

Derived a large set of non-trivial approximate solutions

Extended symmetry analysis to hyperbolic reaction-diffusion-convection equations

Validated the approach with explicit symmetry calculations

Abstract

Within the theoretical framework of a recently introduced approach to approximate Lie symmetries of differential equations containing small terms, which is consistent with the principles of perturbative analysis, we define accordingly approximate Q-conditional symmetries of partial differential equations. The approach is illustrated by considering the hyperbolic version of a reaction-diffusion-convection equation. By looking for its first order approximate Q-conditional symmetries, we are able to explicitly determine a large set of non-trivial approximate solutions.