A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction

A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction

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 thereb...

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Bibliographic Details
Main Authors: Hongli An, Colin Rogers
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2012-08-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
magnetogasdynamic system
elliptic vortex
Hamiltonian-Ermakov structure
Lax pair
Online Access:http://dx.doi.org/10.3842/SIGMA.2012.057
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spelling doaj-3aeabfa3e42a4a8fbc6bc27f729c67122020-11-24T22:39:58ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-08-018057A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable ReductionHongli AnColin RogersA 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.http://dx.doi.org/10.3842/SIGMA.2012.057magnetogasdynamic systemelliptic vortexHamiltonian-Ermakov structureLax pair
collection DOAJ
language English
format Article
sources DOAJ
author Hongli An
Colin Rogers
spellingShingle Hongli An
Colin Rogers
A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
Symmetry, Integrability and Geometry: Methods and Applications
magnetogasdynamic system
elliptic vortex
Hamiltonian-Ermakov structure
Lax pair
author_facet Hongli An
Colin Rogers
author_sort Hongli An
title A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
title_short A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
title_full A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
title_fullStr A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
title_full_unstemmed A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
title_sort 2+1-dimensional non-isothermal magnetogasdynamic system. hamiltonian-ermakov integrable reduction
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2012-08-01
description 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.
topic magnetogasdynamic system
elliptic vortex
Hamiltonian-Ermakov structure
Lax pair
url http://dx.doi.org/10.3842/SIGMA.2012.057
work_keys_str_mv AT honglian a21dimensionalnonisothermalmagnetogasdynamicsystemhamiltonianermakovintegrablereduction
AT colinrogers a21dimensionalnonisothermalmagnetogasdynamicsystemhamiltonianermakovintegrablereduction
AT honglian 21dimensionalnonisothermalmagnetogasdynamicsystemhamiltonianermakovintegrablereduction
AT colinrogers 21dimensionalnonisothermalmagnetogasdynamicsystemhamiltonianermakovintegrablereduction
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