三个方程耦合的Schrödinger方程组的基态  

Ground states of a system of three Schrodinger equations

作　　者：陈新燕 刘海东 刘兆理 Chen Xinyan;Liu Haidong;Liu Zhaoli(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China;Institute of Mathematics,Jiaxing University,Zhejiang 314001,China)

机构地区：[1]首都师范大学数学科学学院,北京100048 [2]嘉兴学院数学研究所,浙江嘉兴314001

出　　处：《纯粹数学与应用数学》2021年第1期1-24,共24页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701220,11926334,11926335,12031015,12026247,11671272);浙江省自然科学基金(LY21A010020).

摘　　要：研究由三个方程耦合的非线性Schrödinger方程组,它们源于非线性光学和Bose-Einstein凝聚.考虑了两种类型:含有周期位势的方程组和含有势阱位势的方程组.借助于广义的Nehari流形以及精细的能量估计,证明了当相互作用位势适当小时,这两类非线性Schrödinger方程组存在正的基态.In this paper we consider a system of three coupled nonlinear Schrödinger equations,which comes from nonlinear optics and Bose-Einstein condensates.We deal with two types:systems with periodic potentials,and systems with trapping potentials.Using the generalized Nehari manifold and delicate energy estimates,we establish the existence of a positive ground state for either type provided that the interacting potentials are suitably small.

关 键 词：基态 非线性Schrödinger方程组 变分方法 

分 类 号：O175.2[理学—数学]