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A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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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, Hamiltonian–Ermakov structure
Mots-clés : elliptic vortex, Lax pair. 
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     author = {Hongli An and Colin Rogers},
     title = {A $2+1$-dimensional non-isothermal magnetogasdynamic system. {Hamiltonian{\textendash}Ermakov} integrable reduction},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a56/}
}
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Hongli An; Colin Rogers. A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a56/

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