Supersymmetric Polytropic Gas Dynamics

TL;DR

This paper develops the N=1 supersymmetric extension of polytropic gas dynamics, providing Lagrangian and Hamiltonian formulations, demonstrating integrability through conserved charges, and comparing it with related supersymmetric systems.

Contribution

It introduces the supersymmetric extension of polytropic gas dynamics, constructs conserved charges, and analyzes integrability and differences with similar models.

Findings

Complete integrability established via conserved charges

Construction of supersymmetric extensions and Hamiltonian structure

Comparison with supersymmetric Chaplygin gas

Abstract

We construct the N=1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of "Eulerian'' conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY -B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N=1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.