Scattering and strong instability of the standing waves for dipolar quantum gases
DOI10.3934/DCDSB.2020297zbMath1471.35257OpenAlexW3092113976MaRDI QIDQ2033802
Publication date: 17 June 2021
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdsb.2020297
Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Soliton equations (35Q51) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of gases (82D05)
Cites Work
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- The threshold for the focusing Gross-Pitaevskii equation with trapped dipolar quantum gases
- Existence of solitary waves in dipolar quantum gases
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Scattering theory in the energy space for a class of nonlinear Schrödinger equations
- Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
- Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
- Scattering in the energy space and below for 3D NLS
- Scattering threshold for the focusing nonlinear Klein-Gordon equation
- Asymptotic dynamic for dipolar quantum gases below the ground state energy threshold
- Exact value of cross-constrain problem and strong instability of standing waves in trapped dipolar quantum gases
- A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
- Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates
- On the Gross–Pitaevskii equation for trapped dipolar quantum gases
- On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3
- Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases
- Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases
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