三个方程耦合的Schrödinger方程组的基态

Ground states of a system of three Schrodinger equations

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.