Search

Based on the traveling wave reduction method with a perturbed initial solution and the F-expansion method, a class of explicit exact solutions of the (2+1)-dimensional CDGKS equation are obtained through the symbolic computation. Moreover, both the interaction behavior between parameters and the perturbation degree of periodic wave and Gauss wave to rational pulse wave, and the correlation of parameters to the superposition degree of the interaction energy between solitary wave and rational pulse wave are discussed. Finally, numerical simulations are shown to demonstrate the mechanism of the above solutions.

In this paper we present a second order numerical scheme for the Cahn-Hilliard equation, with a Fourier pseudo-spectral approximation in space. An additional Douglas-Dupont regularization term is introduced, which ensures the energy stability. The bound of numerical solution in H2h and l? norms are obtained at a theoretical level. Moreover, for the global nature of the pseudo-spectral method, we propose a linear iteration algorithm to solve the non-linear system, due to the implicit treatment for the non-linear term. Some numerical simulations verify the efficiency of iteration algorithm.