Standing waves for the nonlinear Schrodinger equation coupled with the Maxwell equation
Standing waves for the nonlinear Schrodinger equation coupled with the Maxwell equation
复制标题
非线性薛定谔方程与麦克斯韦方程耦合的驻波
DOI：
10.1088/1361-6544/aa6760
复制
发表时间：
2017
期刊：
影响因子：
1.7
通讯作者：
Tatsuya Watanabe
中科院分区：
文献类型：
--
作者：
Mathieu Colin;Tatsuya Watanabe
本文研究了与麦克斯韦方程耦合的非线性薛定谔方程的驻波问题。首先，我们描述的条件下存在的极小与规定的收费方面的耦合常数e。其次，我们研究了定态问题基态的存在性，小e时基态的唯一性以及极小化子与基态之间的联系。最后研究了二次非线性驻波轨道的稳定性。
In this paper, we are interested in standing waves of the nonlinear Schrödinger equation coupled with the Maxwell equation. Firstly we describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e. Secondly we study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and a link between minimizers and ground states. Finally we study the orbital stability of standing waves for the quadratic nonlinearity.