INTEGRABLE SYSTEMS IN HIGHER DIMENSIONS

This article reviews a class of Universal Field Equations which, besid es exhibiting general covariance, are shown to arise from an iterative procedure, starting with a general Lagrangian dependent only on first derivatives of the fields. These equations are integrable using a Leg endre transformation. They arise from consistency requirements on the Lagrangian equations of incompressible fluid flow. Multi-field general isations, and the application to the homogeneous Monge Ampere equation are included. An analysis of the requirement of an infinite number of inequivalent Lagrangian descriptions concludes this review.