Optimal Control for Optical Solitons in Nematic Liquid Crystals

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-08-10 DOI:10.1007/s00245-024-10173-y

Constanza Sánchez de la Vega, Juan Pablo Borgna, Diego Rial

引用次数: 0

Abstract

We study an optimal control problem for a coupled Schrödinger-elliptic evolution system that describes the propagation of a laser beam in nematic liquid crystals. We consider a bilinear control related to an electric field depending on the optical axis acting on the sample. This problem arises from the study of an optimal way to transform the input signal into a target signal by modifying a system parameter related to the bias electric field. We prove well-posedness, existence and first order necessary conditions for an optimal solution.

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向列液晶中光学孤子的优化控制

我们研究了描述激光束在向列液晶中传播的薛定谔-椭圆耦合演化系统的最优控制问题。我们考虑的是与作用在样品上的光轴电场有关的双线性控制。这个问题源于对通过修改与偏置电场相关的系统参数将输入信号转换为目标信号的最佳方法的研究。我们证明了最优解的拟合性、存在性和一阶必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.