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

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