Reciprocal Transformations in Relativistic Gasdynamics. Lie Group Connections

TL;DR

This paper explores how reciprocal transformations, linked to Lie group methods, reveal invariance properties in relativistic gasdynamics, extending their physical and mathematical applications from non-relativistic contexts.

Contribution

It establishes a connection between reciprocal transformations and Lie group procedures in the context of relativistic gasdynamics, broadening the understanding of invariance properties.

Findings

Reciprocal transformations relate to invariance in relativistic gasdynamics.

Lie group methods are used to analyze these transformations.

The approach links to physical applications and integrable systems.

Abstract

Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently been shown to have diverse physical applications to nonlinear systems, notably in the analytic treatment of Stefan-type moving boundary problem and in linking inverse scattering systems and integrable hierarchies in soliton theory. Here,invariance under classes of reciprocal transformations in relativistic gasdynamics is shown to be linked to a Lie group procedure.