Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases

摘要

We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding constrained minimization problem and establish existence, symmetry and uniqueness of the ground state solutions.