Curve-like concentration for Bose-Einstein condensates

作者：Guo, Qing; Tian, Shuying^*; Zhou, Yang

来源：Calculus of Variations and Partial Differential Equations, 2022, 61(2): 63.

DOI：10.1007/s00526-021-02171-7

• SCHRODINGER-EQUATIONS
• NOBEL LECTURE
• STATES
• VORTEX
• GAS

This article is devoted to studying the model of Bose-Einstein condensates (BECs) with attractive interactions, and it can be described by Gross-Pitaevskii energy functional with L-2-constraint for the mass. Recently, the solutions of this model concentrated at several points have been widely considered. However, it does not seem to have the result on solutions concentrating at a high dimensional subset. In this paper, we show that the existence of radial solutions of the model concentrating on spheres under suitable conditions by using modified finite dimensional reduction and blow-up analysis based on Pohozaev identity. Also we would like to point out that this concentration phenomena is quite different from those of classical nonlinear Schrodinger equations.

• 单位
  武汉理工大学