Decay for travelling waves in the Gross-Pitaevskii equation

DOI10.1016/j.anihpc.2003.09.001zbMath1057.35060OpenAlexW2003948488MaRDI QIDQ1886254

Philippe Gravejat

Publication date: 18 November 2004

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_5_591_0

zbMATH Keywords

Nonlinear Schrödinger equationTravelling wavesDecay at infinity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Statistical mechanics of superconductors (82D55) NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of superfluids (82D50)

Related Items (17)

Smooth branch of travelling waves for the Gross-Pitaevskii equation in R2 for small speed ⋮ Invariant manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space ⋮ Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity ⋮ The Cauchy problem for the Gross--Pitaevskii equation ⋮ A uniqueness result for travelling waves in the Gross-Pitaevskii equation ⋮ Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d ⋮ Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation ⋮ Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains ⋮ A uniqueness result for the two-vortex traveling wave in the nonlinear Schrödinger equation ⋮ Coercivity for travelling waves in the Gross-Pitaevskii equation in \(\mathbb{R}^2\) for small speed ⋮ Vortex rings for the Gross-Pitaevskii equation ⋮ A lower bound on the energy of travelling waves of fixed speed for the Gross-Pitaevskii equation ⋮ Global Well-Posedness for a Nonlocal Gross–Pitaevskii Equation with Non-Zero Condition at Infinity ⋮ Travelling waves for the Gross-Pitaevskii equation. II ⋮ ASYMPTOTIC AXISYMMETRY OF THE SUBSONIC TRAVELING WAVES TO THE GROSS–PITAEVSKII EQUATION ⋮ Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime ⋮ Limit at infinity for travelling waves in the Gross-Pitaevskii equation.

Cites Work

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• Decay and analyticity of solitary waves
• From Ginzburg-Landau to Gross-Pitaevskii
• A non-existence result for supersonic travelling waves in the Gross-Pitaevskii equation
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Vortex rings for the Gross-Pitaevskii equation
• Analyticity and decay properties of the solitary waves to the Benney-Luke equation.
• Limit at infinity for travelling waves in the Gross-Pitaevskii equation.
• Travelling waves for the Gross-Pitaevskii equation. II
• On multipliers of Fourier integrals in the spaces \(L_{p,\theta}\)
• Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves

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