Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity
DOI10.3934/dcds.2020026zbMath1431.35170arXiv1812.08713OpenAlexW2981262758MaRDI QIDQ2281589
Pierre Mennuni, André De Laire
Publication date: 3 January 2020
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.08713
traveling wavesGross-Pitaevskii equationorbital stabilitydark solitonsnonlocal Schrödinger equationnonzero conditions at infinity
Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence theories for optimal control problems involving partial differential equations (49J20) Variational methods for second-order elliptic equations (35J20) Traveling wave solutions (35C07) Soliton solutions (35C08) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)
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Cites Work
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- Stability in the energy space for chains of solitons of the Landau-Lifshitz equation
- Existence of solitary waves in dipolar quantum gases
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- The Cauchy problem for the Gross--Pitaevskii equation
- Non-existence for travelling waves with small energy for the Gross-Pitaevskii equation in dimension \(N \geqslant 3\)
- Functional analysis, Sobolev spaces and partial differential equations
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
- On a class of non linear Schrödinger equations with non local interactions
- Stability and instability of traveling solitonic bubbles.
- Vortex rings for the Gross-Pitaevskii equation
- Elliptic partial differential equations of second order
- The sine-Gordon regime of the Landau-Lifshitz equation with a strong easy-plane anisotropy
- Ground states for a nonlocal mixed order cubic-quartic Gross-Pitaevskii equation
- Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions
- Stability and instability for subsonic traveling waves of the nonlinear Schrödinger equation in dimension one
- Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
- Symmetry of minimizers for some nonlocal variational problems
- Travelling waves for the Gross-Pitaevskii equation. II
- Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
- Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
- On Dipolar Quantum Gases in the Unstable Regime
- On some minimization problems in RN
- Nonexistence of traveling waves for a nonlocal Gross--Pitaevskii equation
- Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension one
- Asymptotic stability of the black soliton for the Gross–Pitaevskii equation
- Global Well-Posedness for a Nonlocal Gross–Pitaevskii Equation with Non-Zero Condition at Infinity
- The KdV/KP-I Limit of the Nonlinear Schrödinger Equation
- Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data
- SCATTERING THEORY FOR THE GROSS–PITAEVSKII EQUATION IN THREE DIMENSIONS
- Classical Fourier Analysis
- The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity
- On the Gross–Pitaevskii equation for trapped dipolar quantum gases
- Orbital stability of the black soliton for the Gross-Pitaevskii equation
- Nonexistence of Supersonic Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity
- Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
- Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence
- Motions in a bose condensate: VI. Vortices in a nonlocal model
- On the Korteweg-de Vries Long-Wave Approximation of the Gross-Pitaevskii Equation I
- Small energy traveling waves for the Euler–Korteweg system
- Existence and properties of travelling waves for the Gross-Pitaevskii equation
- Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity
- Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity
- Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
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