Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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