Global Attractor For A Class Of Coupled Nonlinear Schr(?)dinger Equations

This paper mainly studies the zero order long time in behavior of the dissipative coupling nonlinear Schrodinger equations. At the first chapter, we mainly introduce the process of development of dynamical system and the status quo at home and abroad, which simply describes some basic concepts and research methods, as well as the research background, etc. At the second chapter, the global weak attractor for this system in Hper2(Ω)×Hper2(Ω) is constructed on what is based on a prior estimate. And then by exact analysis of the energy equation. It is shown that the global weak attractor is actually the global strong attractor in Hper2(Ω)×Hper(Ω). At the third chapter, we estimate uniform Lyapunov exponents of this attractor to prove its finite fractal dimensional character and the Hausdorff dimensional character.