Jordan canonical forms for systems of elliptic equations

Abstract

This work involves the study of elliptic type systems of equations in three independent variables. The Lie point symmetries of the systems are obtained; some of the symmetries of a particular system are used to perform reduction to an invariant system with one less independent variable. The symmetries of the reduced system are also obtained and used for further reduction to a system of ordinary differential equations (ODEs). The invariant solutions of the system of ODEs are constructed.