Abstract

Problem review of existence and stability nonlinear parabolic functionally differential equations structures with transformation of spatial variables. Such equations model optical systems that contain a thin layer of a nonlinear Kerr-type medium. Review of Initial boundary value problems for circumference, a circle, and a ring with an involution operator, corresponding to transformation of variables (rotation). The asymptotics of solutions are constructed using the method of central manifolds. Analysis of Metastable structures and slowly changing solutions. Approximate solutions are found using Galerkin approximations. Presentation of the results for numerical experiments.

中文翻译：

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带空间变量变换的非线性抛物方程的稳定结构

摘要

具有空间变量变换的非线性抛物线泛函微分方程结构的存在性和稳定性问题回顾。此类方程对包含非线性克尔型介质薄层的光学系统进行建模。回顾圆周、圆和具有对合算子的环的初始边界值问题，对应于变量的变换（旋转）。解的渐近线是使用中心流形的方法构造的。分析亚稳态结构和缓慢变化的解决方案。近似解是使用伽辽金近似找到的。数值实验结果的介绍。