Dynamics Of Solutions To The Lattice Nonlinear Schrodinger Type Equations

Lattice dynamical systems are spatiotemporal systems with dis-cretization of some variables, including coupled ordinary diferentialequations, coupled map lattices and cellular automata. Nowadays,some basic theories of lattice dynamical systems have already beenestablished. As the importance of the lattice dynamical systems inpractical applications, it has been studied by many academicians andthey have got many useful results.This paper studies the dynamics of the lattice coupled nonlinearSchroodinger-Boussinesq equations and the lattice coupled nonlinearSchroodinger equations. The paper consists of four chapters.In the frst chapter, we frst introduce the origin of infnite di-mensional dynamical system, lattice dynamical system, and researchpresent status is also given. Then we present the main research con-tents.In Chapter2, we study the asymptotic behaviour of solutionsto the lattice coupled nonlinear Schroodinger-Boussinesq equations.We frst prove the existence of the global attractor for the generatedsemigroup and then obtain an upper bound of the Kolmogorov-entropy for the obtained global attractor. Finally, we establish theupper semicontinuity of the global attractor when the infnite latticesystems are approximated by fnite lattice systems.In Chapter3, we consider the asymptotic behavior of solutionsto the lattice dynamical system corresponding to the coupled lattice nonlinear Schroodinger equations. We prove the existence of the uni-form attractor in some proper sense according to the characteristicsof equations and then obtain an upper bound of the Kolmogorov-entropy for the obtained uniform attractor.In the last chapter, we summarize the paper.