Exponential Attractors Of Nonlinear Schr(o|")dinger Lattice Equation

The main content of this paper is to prove the existence of an exponential attrac-tor, a pullback exponential attractor and a uniform exponential attractor for nonlinear Schrodinger lattice equation. The exponential attractor is an important concept in the asymptotic behavior of the dynamical systems of infinite dimensional dynamics. In re-cent years, there are many works for the exponential attractors of the dynamical system. Moreover, the problem of the existence of exponential attractor, pullback attractor and uniform exponential attractor for non-autonomous dynamical system attracts scholars attention at home and abroad. This paper mainly consists of four chapters:In chapter 1, this paper introduces the development survey of lattice dynamical system. Then the necessity and its important meaning of the existence of exponential attractor, pullback exponential attractor and uniform exponential attractor for the dy-namical system will be discussed. At last, the paper introduces the newest research status of nonlinear Schrodinger lattice system and the main content of this paper.In chapter 2, we will apply some sufficient conditions for the existence of an ex-ponential attractor to prove the existence of an exponential attractor for the nonlinear Schrodinger lattice equation.In chapter 3, we will apply some sufficient conditions for the existence of a pull-back exponential attractor to prove the existence of a pullback exponential attractor for the non-autonomous nonlinear Schrodinger lattice equation effected by time-dependent coupled coefficients and forces.In chapter 4. we will apply some sufficient conditions for the existence of a uniform exponential attractor to prove the existence of a uniform exponential attractor for the non-autonomous nonlinear Schrodinger lattice equation driven by quasi-periodic external forces.