Reduction of systems of two nonlinear parabolic type partial differential equations to solvable forms using differential invariants

Abstract

Differential invariants for linear and nonlinear ordinary and partial differential equations have been derived using Lie infinitesimal method. These invariants help in reducing differential equations to their simplest possible solvable forms through invertible transformations of the dependent and independent variables. Here we derive differential invariants for a class of systems of two second order nonlinear parabolic type partial differential equations. Deduced invariants are shown to reveal solvable forms of these systems of PDEs that are much simpler than the considered general systems of nonlinear parabolic type PDEs.