New exact homoclinic wave and periodic wave solutions for the Ginzburg–Landau equation

摘要

New exact solutions including homoclinic wave and periodic wave solutions for the 2D Ginzburg–Landau equation are obtained using the auxiliary function method and the G′G-expansion method, respectively. The solutions are expressed by the hyperbolic functions and the trigonometric functions. There result shows that there exists a kink wave solution which tends to one and the same periodic wave solution as time tends to infinite.