A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction

TL;DR

This paper demonstrates that a 2+1-dimensional magnetogasdynamic system with a polytropic gas law admits an integrable reduction to a Hamiltonian-Ermakov system, enabling exact solutions describing rotating elliptic plasma cylinders.

Contribution

It introduces an integrable elliptic vortex reduction for the magnetogasdynamic system at b3=2, revealing a novel Hamiltonian-Ermakov structure and exact solutions.

Findings

Exact solutions for rotating elliptic plasma cylinders.

Elliptic cross-section axes satisfy an Ermakov-Ray-Reid system.

Identification of Hamiltonian-Ermakov integrable structure.

Abstract

A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when $\gamma=2$ to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical cross-section, remarkably, satisfy a Ermakov-Ray-Reid system.