Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
From MaRDI portal
Publication:486740
DOI10.5802/aif.2838zbMath1337.35131arXiv1206.2221OpenAlexW2950308022MaRDI QIDQ486740
Philippe Gravejat, Didier Smets, Fabrice Bethuel
Publication date: 16 January 2015
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1206.2221
Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)
Related Items
Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons, On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation, On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions, Orbital stability of the sum of smooth solitons in the Degasperis-Procesi equation, Recent results for the Landau-Lifshitz equation, Asymptotic stability of Zakharov-Kuznetsov solitons, Stability of solitons of the Landau-Lifshitz equation with planar anisotropy, Leapfrogging vortex rings for the three dimensional Gross-Pitaevskii equation, Asymptotic stability of the black soliton for the Gross–Pitaevskii equation, On the stability of the Ginzburg–Landau vortex, Stability in the energy space for chains of solitons of the Landau-Lifshitz equation, On the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equation, On the Cauchy Problem and the Black Solitons of a Singularly Perturbed Gross--Pitaevskii Equation, Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations, Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity, Existence of multi-travelling waves in capillary fluids
Cites Work
- Unnamed Item
- Stability of two soliton collision for nonintegrable gKdV equations
- The Cauchy problem for the Gross--Pitaevskii equation
- Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
- Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
- Stability theory of solitary waves in the presence of symmetry. I
- Stability and instability of traveling solitonic bubbles.
- Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation with finite-density initial data. II: Dark solitons on continua
- Stability and asymptotic stability for subcritical gKdV equations
- Inelastic interaction of nearly equal solitons for the quartic gKdV equation
- Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
- Schrödinger group on Zhidkov spaces
- Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension one
- The KdV/KP-I Limit of the Nonlinear Schrödinger Equation
- On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II
- Orbital stability of the black soliton for the Gross-Pitaevskii equation
- The Korteweg–deVries Equation: A Survey of Results
- On the Korteweg-de Vries Long-Wave Approximation of the Gross-Pitaevskii Equation I
- Existence and properties of travelling waves for the Gross-Pitaevskii equation
- Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
