Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases
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Publication:4921876
DOI10.4153/CMB-2011-181-2zbMath1264.35223MaRDI QIDQ4921876
Publication date: 28 May 2013
Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)
NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44)
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Finite time blow-up for the nonlinear Schrödinger equation in trapped dipolar quantum gases with arbitrarily positive initial energy ⋮ Cross-invariant manifolds for the Gross-Pitaevskii-Poisson equation ⋮ Exact value of cross-constrain problem and strong instability of standing waves in trapped dipolar quantum gases ⋮ Strong instability of standing waves for the nonlinear Schrödinger equation in trapped dipolar quantum gases ⋮ Blow up threshold for the Gross‐Pitaevskii system with trapped dipolar quantum gases ⋮ Sufficient conditions of collapse for dipolar Bose‐Einstein condensate ⋮ On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions ⋮ Scattering and strong instability of the standing waves for dipolar quantum gases ⋮ Blow up threshold for the Gross-Pitaevskii system with combined nonlocal nonlinearities ⋮ Invariant sets and the blow up threshold for coupled systems of reaction–diffusion ⋮ Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases
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