From infinitesimal symmetries to deformed symmetries of Lax-type equations

TL;DR

This paper introduces a method to deform Lax-type equations via time scaling, resulting in integrable equations expressed as power series, and identifies a Lie group of symmetries for these deformed equations.

Contribution

It presents a novel deformation approach for Lax-type equations using time scaling and characterizes their symmetry group within a regular Frölicher Lie group framework.

Findings

Deformed equations remain integrable as power series in the scaling parameter.

A regular Frölicher Lie group of symmetries is constructed for the deformed equations.

The method generalizes previous symmetry analysis of Lax equations.

Abstract

Using the procedure initiated in \cite{Ma2013}, we deform Lax-type equations though a scaling of the time parameter. This gives an equivalent (deformed) equation which is integrable in terms of power series of the scaling parameter. We then describe a regular Fr\"olicher Lie group of symmetries of this deformed equation