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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...
Based on the approximate symmetry group method, the differential form Wu's method and a generalized Riccati equation with variable coefficients expansion method, a hybrid approach for obtaining the approximate solitary wave solutions of a perturbed BBM equations is introduced.
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