Hidden integrability in ideal magnetohydrodynamics: The Pohlmeyer–Lund–Regge model

Abstract

It is shown that the equilibrium equations of ideal magnetohydrodynamics reduce to the integrable Pohlmeyer–Lund–Regge model subject to a volume-preserving constraint if the Maxwellian surfaces are assumed to coincide with the constant total pressure surfaces. It is demonstrated that any solution of the constrained Pohlmeyer–Lund–Regge model gives rise to a multiplicity of solutions of the magnetohydrodynamic system which share the streamline and magnetic field line geometry. Explicit solutions given in terms of elliptic functions and integrals are constructed.