Symmetry Reduction and Exact Solutions of the Euler–Lagrange–Born–Infeld, Multidimensional Monge–Ampere and Eikonal Equations

Abstract

Using the subgroup structure of the generalized Poincaré group P (1, 4), ansatzes which reduce the Euler–Lagrange–Born–Infeld, multidimensional Monge–Ampere and eikonal equations to differential equations with fewer independent variables have been constructed. Among these ansatzes there are ones which reduce the considered equations to linear ordinary differential equations. The corresponding symmetry reduction has been done. Using the solutions of the reduced equations, some classes of exact solutions of the investigated equation have been presented.