A two-dimensional magnetohydrodynamic system: geometric decomposition and canonical reduction

Abstract

AbstractA geometric decomposition previously adopted in areas of nonlinear continuum mechanics and soliton theory is applied to a two-dimensional time-independent magnetohydrodynamic system to obtain reduction to a canonical third order nonlinear equation subject to a constraint. Novel classes of exact solutions to the magnetohydrodynamic system are thereby constructed. Connection is made with kinematic conditions which attend certain steady two-dimensional motions of fibre-reinforced viscous fluids.