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

Rémi Carles (1) , Hichem Hajaiej (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 KSU - King Saud University [Riyadh]

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Rémi Carles, Hichem Hajaiej. Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases. Bulletin of the London Mathematical Society, 2015, 47 (3), pp.509-518. ⟨10.1112/blms/bdv024⟩. ⟨hal-00953716⟩