Hongli An, Colin Rogers, “A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction”, SIGMA, 2012, том 8,057, 15 стр.

Эта публикация цитируется в 4 статьях

A $2+1$-dimensional non-isothermal magnetogasdynamic system. Hamiltonian–Ermakov integrable reduction

Hongli An^a, Colin Rogers^bc

^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

Аннотация: 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.

Ключевые слова: magnetogasdynamic system, elliptic vortex, Hamiltonian–Ermakov structure, Lax pair.

MSC: 34A34; 35A25

Поступила: 27 мая 2012 г.; в окончательном варианте 2 августа 2012 г.; опубликована 23 августа 2012 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2012.057