Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/7671
Title: The pulsrodon in 2+1-dimensional magneto-gasdynamics : Hamiltonian structure and integrability
Authors: Rogers, C
Schief, WK
Keywords: Two-dimensional magnetohydrodynamic equations
Time-dependent solutions
Ermakov systems
Nonlinear superposition
Similarity solutions
Mhd equations
Plasma
Oscillations
Principles
Issue Date: Aug-2011
Publisher: American Institute of Physics
Source: Journal of mathematical physics, Aug. 2011, v. 52, no. 8, 083701, p. 1-20 How to cite?
Journal: Journal of mathematical physics 
Abstract: An elliptic vortex-type ansatz introduced into a 2+1-dimensional system governing rotating homentropic magneto-gasdynamics with a parabolic gas law is shown to lead to a finite-dimensional nonlinear dynamical system which admits exact analytical solution in terms of an elliptic function and integral representation. The dynamical system is demonstrated to be Hamiltonian and equivalent to the stationary reduction of the integrable nonlinear Schrödinger equation coupled with a Steen-Ermakov-Pinney equation. A novel magneto-gasdynamic analogue of the pulsrodon of shallow water f-plane theory is isolated thereby. Confined and time-periodic magneto-gasdynamic flows are constructed explicitly.
URI: http://hdl.handle.net/10397/7671
ISSN: 0022-2488 (print)
1089-7658 (online)
DOI: 10.1063/1.3622595
Rights: © 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in C. Rogers and W. K. Schief, J. Math. Phys., 52, 083701 (2011) and may be found at http://link.aip.org/link/?jmp/52/083701
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