非线性光学中薛定谔型方程的整体吸引子

张瑞凤, 寇汴闽

数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 17-26.

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数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 17-26. DOI: 10.12386/A2012sxxb0002
论文

非线性光学中薛定谔型方程的整体吸引子

    张瑞凤1, 寇汴闽2
作者信息 +

Global Attractors for Schrödinger Equation Arising in Nonlinear Optics

    Rui Feng ZHANG1, Bian Min KOU2
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摘要

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.  

Abstract

We study a nonlinear Schrödinger 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.  

关键词

薛定谔方程 / 整体吸引子 / 分形维数和 Hausdorff维数

Key words

Schrödinger equation / global attractor / the fractal and Hausdorff dimensions

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导出引用
张瑞凤, 寇汴闽. 非线性光学中薛定谔型方程的整体吸引子. 数学学报, 2012, 55(1): 17-26 https://doi.org/10.12386/A2012sxxb0002
Rui Feng ZHANG, Bian Min KOU. Global Attractors for Schrödinger Equation Arising in Nonlinear Optics. Acta Mathematica Sinica, Chinese Series, 2012, 55(1): 17-26 https://doi.org/10.12386/A2012sxxb0002

参考文献

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基金

河南省自然科学基金资助项目(112300410054)

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