A Method to Construct Asymptotic Solutions Invariant under the Renormalization Group

TL;DR

This paper introduces a renormalization group method combined with Lie symmetry techniques to derive asymptotic solutions that remain invariant under the approximate symmetries of perturbed differential equations.

Contribution

It presents a novel approach integrating Lie symmetry with renormalization group methods to construct invariant asymptotic solutions for singular perturbation problems.

Findings

Successfully derives group-invariant asymptotic solutions.

Extends renormalization group techniques with Lie symmetry.

Applicable to singular perturbation problems.

Abstract

A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential equations.