非线性光学晶格中的梯度流方法

Gradient Flow Method in Nonlinear Optical Lattices

该文利用梯度流方法研究非线性光学晶格中经典薛定谔方程稳态解的存在性.文中首先给出了控制方程整体解的存在性,然后证明了当时间趋于无穷大时整体解收敛到一个平衡态(即光学晶格模型的稳态解).此外,通过Lojasiewicz-Simon不等式给出了收敛速度估计.

In this paper,we study the existence of the steady state solutions for a classical Schr(o|")dinger equation in nonlinear optical lattices by means of gradient flow method.We first establish the existence of a global solution of the governing parabolic equation.Then we prove the convergence of the global solution to an equilibrium(i.e.,a steady state solution in optical lattices model) as time goes to infinity.Furthermore,we provide an estimate on the convergence rate by using the Lojasiewicz-Simon inequality.