SIGMA 8 (2012), 057, 15 pages      arXiv:1208.4666      https://doi.org/10.3842/SIGMA.2012.057
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”

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

Hongli An ^a and Colin Rogers ^{b, c
a)} College of Science, Nanjing Agricultural University, Nanjing 210095, P.R. China
^b) School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia
^c) Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Sydney, NSW2052, Australia

Received May 27, 2012, in final form August 02, 2012; Published online August 23, 2012

Abstract
A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ=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.

Key words: magnetogasdynamic system; elliptic vortex; Hamiltonian-Ermakov structure; Lax pair.

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