Approximate Solutions and Symmetry Group for Initial-Value Problem of Nonlinear Cahn-Hilliard Equation

Abstract: In this paper , for the nonlinear Cahn-Hilliard equation, we give its symmetry group by the approximate generalized conditional symmetry. As the application of approximate generalized conditional symmetry, the initial-value problem of the partial differential equations can be reduced to perturbed initial-value problem for a system of perturbed first-order ordinary differential equations. By solving the reduced ordinary differential equations, we obtain the approximate solutions of the initial-value problem of research equations. At the last, some exaples be given to show the reduction procedure.