Conservation laws for some systems of nonlinear PDEs via the symmetry/adjoint symmetry pair method

This paper applies the symmetry/adjoint symmetry pair method to find conservation laws for nonlinear partial differential equations. As examples, conservation laws are obtained for a combined potential system (with nonlinear telegraph and nonlinear diffusion-convection equations as special cases) as well as for an extended nonlinear wave equation system. In addition, for both examples, conservation laws are obtained for and nonlocally related equivalent systems. The paper concludes with a posed open problem.