Lie symmetry analysis and conservation laws of systems of elliptic equations

Abstract

This work involves the study of elliptic type systems of equations in three independent variables. In the first part of the work, the Lie point symmetries of the systems are obtained; some of the symmetries of a system are used to perform reduction to an invariant system with one less independent variable. The symmetries of the invariant system are also obtained and used for further reduction to a system with one more less independent variable. The invariant solutions of the last reduced system are constructed. The second par t of this study deal s with the construction of conservation laws of the systems of elliptic equations. The variational approach is used, that is, the Noether point symmetries and their corresponding conserved vectors are obtained.