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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 057, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.057 (Mi sigma734) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2012.057
URL: https://emis.mi.ras.ru/journals/SIGMA/2012/057
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
Bibliographic databases:
Document Type: Article
MSC: 34A34; 35A25
Language: English
Citation: Hongli An, Colin Rogers, “A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction”, SIGMA, 8 (2012), 057, 15 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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