Derivation of conservation laws for a nonlinear wave equation modelling melt migration using Lie point symmetry generators

The derivation of conservation laws for a nonlinear wave equation modelling the migration of melt through the Earth’s mantle is considered. New conserved vectors which depend explicitly on the spatial coordinate are generated using the Lie point symmetry generators of the equation and known conserved vectors. It is demonstrated how conserved vectors that are conformally associated with a Lie point symmetry generator can be derived more simply than by the direct method by imposing the symmetry condition on the conservation law equation.