非线性光学中薛定谔型方程的整体吸引子

Global Attractors for SchrSdinger Equation Arising in Nonlinear Optics

研究了一类非线性薛定谔型方程,描述了光波在光折射晶体中的传播.首先构造了该模型整体弱的吸引子,然后通过能量方程的精确分析,证明整体弱吸引子实际为系统整体强吸引子.最后给出了整体吸引子的分形维数和Hausdorff维数的上界估计.

We study a nonlinear Schrodinger equation modeling light waves propagating in a photorefractive crystal.We first construct the global weak attractor for this system.And then by exact analysis of the energy equation,we show that the global weak attractor is actually the global strong attractor.Further,we give the upper bound of the fractal and Hausdorff dimensions of the global attractor.