1208.4666 (Hongli An et al.)

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

Hongli An, Colin Rogers

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.

View original: http://arxiv.org/abs/1208.4666