Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation

With the assistance of the symboliccomputation system Maple, rich higher order polynomial-typeconservation laws and a sixth order t/x-dependent conservationlaw are constructed for a generalized seventh order nonlinearevolution equation by using a direct algebraic method. From thecompatibility conditions that guaranteeing the existence ofconserved densities, an integrable unnamed seventh order KdV-typeequation is found. By introducing some nonlinear transformations,the one-, two-, and three-solition solutions as well as thesolitary wave solutions are obtained.