On three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates with trapping potentials

Abstract

We are concerned with the three-component generalized Gross-Pitaevskii Equations (GGPE) in the spinor Bose-Einstein condensates with trapping potentials. Under certain conditions on trapping potentials and parameters, we establish the existence and uniqueness of corresponding standing wave solutions with behaviors tending to zero at infinity. The same issues for the corresponding Dirichlet boundary value problems on the ball centered at the origin are also concluded. Additionally, we provide a classification of various types of solutions to radially symmetric situations.