Symmetry reduction and exact solutions of the multidimensional monge-ampere equation

Abstract

By using the subgroup structure of the generalized Poincare groupP( 1, 4), we perform a symmetry reduction of the multidimensional Monge-Ampere equation to differential equations with a smaller number of independent variables. On the basis of solutions of the reduced equations, we construct some classes of exact solutions of the equation under consideration.