A constrained variational problem arising in attractive Bose-Einstein condensate with ellipse-shaped potential

DOI10.1016/j.aml.2018.07.023zbMath1410.35198OpenAlexW2884334716MaRDI QIDQ1726489

Huan-Song Zhou, Helin Guo

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.023

zbMATH Keywords

energy estimatesminimization problemvariational methodelliptic equationellipse-shaped potential

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Phase transitions (general) in equilibrium statistical mechanics (82B26) PDEs in connection with statistical mechanics (35Q82)

Related Items (7)

Limit behavior of attractive Bose-Einstein condensates passing an obstacle ⋮ Ground states of two-component Bose–Einstein condensates passing an obstacle ⋮ Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation ⋮ Unnamed Item ⋮ On supercritical nonlinear Schrödinger equations with ellipse-shaped potentials ⋮ Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials ⋮ Excited states of Bose-Einstein condensates with degenerate attractive interactions

Cites Work

• Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
• Eigenvalue problem for a \(p\)-Laplacian equation with trapping potentials
• Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions
• Asymptotic properties of standing waves for mass subcritical nonlinear Schrödinger equations
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Existence and uniqueness of normalized solutions for the Kirchhoff equation
• On the mass concentration for Bose-Einstein condensates with attractive interactions
• Ground states of nonlinear Choquard equations with multi-well potentials
• Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials
• Stability of attractive Bose-Einstein condensates

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