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SIGMA, 2012, Volume 8, 057, 15 pages (Mi sigma734)  

This article is cited in 2 scientific papers (total in 2 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.

DOI: https://doi.org/10.3842/SIGMA.2012.057

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Full text: http://emis.mi.ras.ru/.../057
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Bibliographic databases:

MSC: 34A34; 35A25
Received: May 27, 2012; in final form August 2, 2012; Published online August 23, 2012
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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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\by Hongli An, Colin Rogers
\paper A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian--Ermakov integrable reduction
\jour SIGMA
\yr 2012
\vol 8
\papernumber 057
\totalpages 15
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\crossref{https://doi.org/10.3842/SIGMA.2012.057}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865826279}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. An H., Fan E., Zhu H., “Elliptical Vortex Solutions, Integrable Ermakov Structure, and Lax pair Formulation of the Compressible Euler Equations”, Phys. Rev. E, 91:1 (2015), 013204  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. An H. Kwong M.K. Zhu H., “On Multi-Component Ermakov Systems in a Two-Layer Fluid: Integrable Hamiltonian Structures and Exact Vortex Solutions”, Stud. Appl. Math., 136:2 (2016), 139–162  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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