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This article is cited in 4 scientific papers (total in 4 papers)
A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction
Hongli Ana, Colin Rogersbc 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
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.
Keywords:
magnetogasdynamic system, elliptic vortex, Hamiltonian–Ermakov structure, Lax pair.
Received: May 27, 2012; in final form August 2, 2012; Published online August 23, 2012
Citation:
Hongli An, Colin Rogers, “A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction”, SIGMA, 8 (2012), 057, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma734 https://www.mathnet.ru/eng/sigma/v8/p57
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Abstract page: | 166 | Full-text PDF : | 39 | References: | 42 |
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