Ground states for a nonlocal cubic-quartic Gross-Pitaevskii equation

Abstract

We prove existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. Using a mountain pass argument on spheres and constructing appropriately localized Palais-Smale sequences we are able to prove existence of real positive ground states as saddle points. The analysis is deployed in the set of possible states, thus overcoming the problem that the energy is unbounded below. We also prove a corresponding nonlocal Pohozaev identity with no rest term, a crucial part of the analysis.

References in corpus (5)

• Observing the Rosensweig instability of a quantum ferrofluid
• Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
• On dipolar quantum gases in the unstable regime
• Striped states in a many-body system of tilted dipoles
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Cited by in corpus (4)

• Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity
• Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction
• Ground states for 3D dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses
• Scattering of the energy-critical NLS with dipolar interaction