New conservation laws of some third-order systems of pdes arising from higher-order multipliers

In this paper, we study conservation laws for some third-order systems of pdes, viz., some versions of the Boussinesq equations and the BBM 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 flows with respect to the Lie point symmetry generators are investigated via the symmetry action on the multipliers.