The pulsrodon in 2+1-dimensional magneto-gasdynamics : Hamiltonian structure and integrability

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.