The Related Research Of Nonlinear Coupled Ginzburg-Landau Equations

This thesis is devoted to the studies of global attractors and periodic wave solutions of both one dimensional and two dimensional nonlinear coupled Ginzburg-Landau equations with variable coefficients by means of the classical Galerkin approximation method, energy method and the F-expansion method.The paper is composed of four chapters.In the first chapter, the historical background and meaning of Ginzburg-Landau equations are presented. Meanwhile, the main works and results of the paper are simply introduced in this part.In the second chapter, we introduce some basic concepts and notations which will be employed in this paper. The basic concepts conclude the related definitions and some important inequalities.In the third chapter, the existence of the global attractor of one dimensional nonlinear coupled Ginzburg-Landau equations is considered firstly. By using the classical Galerkin approximation method, the existence and uniqueness of global solutions are obtained, and thus, the existence of global attractor is obtained by using energy method. Secondly, we also obtain the exact periodic wave solutions of one dimensional nonlinear coupled Ginzburg-Landau equations with constant coefficients by means of F-expansion method and some other skills in this part.In Chapter 4, the global attractor and periodic wave solutions of two dimensional nonlinear coupled Ginzburg-Landau equations are studied. Similar to that in the third chapter, by using classical Galerkin approximation method, we proved the existence and uniqueness of global solutions. Then, the global attractor is obtained by means of energy method. At last, the exact periodic wave solutions is also obtained.