Symmetries and conservation laws of high-order systems of partial differential equations

Abstract

Conservation laws for nonlinear partial di erential equations (pdes) have been determined through di erent approaches. In this dissertation, we study conservation laws for some third-order systems of pdes, viz., some versions of the Boussinesq equations, as well as a version of the BBM equation and the wellknown Ito equation. It is shown that new and interesting conserved quantities arise from `multipliers' that are of order greater than one in derivatives of the dependent variables. Furthermore, the invariance properties of the conserved

ows with respect to the Lie point symmetry generators are investigated via the symmetry action on the multipliers.