aSchool of Mathematics and Information Science, WenZhou University, ZheJiang, 325035, People’s Republic of China
bDepartment of Applied Mathematics, ShangHai Normal University, ShangHai, 200234, People’s Republic of China
Abstract:
In this work, the authors first show the existence of global attractors for the following lattice complex Ginzburg–Landau equation:
and for the following lattice Schrödinger equation:
Then they prove that the solutions of the lattice complex Ginzburg–Landau equation converge to that of the lattice Schrödinger equation as ε→0+. Also they prove the upper semicontinuity of as ε→0+ in the sense that .