Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation**The project supported by the Research Found for the Doctoral Program of the Higher Education of China under Grant No. 20020269003 and the Natural Science Foundation of Shanghai and the “Shu-Guang” Project of Shanghai

Abstract

With the assistance of the symbolic computation system Maple, rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method. From the compatibility conditions that guaranteeing the existence of conserved densities, an integrable unnamed seventh order KdV-type equation is found. By introducing some nonlinear transformations, the one-, two-, and three-solition solutions as well as the solitary wave solutions are obtained.