New higher-order conservation laws of some classes of wave and Gordon-type equations

Abstract

A large class of wave equations, with dissipation and source terms (Gordon type equations), are analysed using a symmetry approach and constructing conservation laws. We obtain some, previously unknown, relationships between the conservation laws and symmetries in the former case. In the latter case, we use the multiplier (and homotopy) approach to construct conservation laws from which some surprisingly, interesting higher-order variational symmetries and corresponding conserved quantities are obtained for a large class of Gordon type equations similar to those of the sine-Gordon equation.