Error bounds for the (KdV)/(KP-I) and (gKdV)/(gKP-I) asymptotic regime for nonlinear Schrödinger type equations

DOI10.1016/j.anihpc.2013.08.007zbMath1307.35274OpenAlexW2067034951MaRDI QIDQ477444

David Chiron

Publication date: 9 December 2014

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

Full work available at URL: https://doi.org/10.1016/j.anihpc.2013.08.007

zbMATH Keywords

nonlinear Schrödinger equationLandau-Lifshitz equationGross-Pitaevskii equationasymptotic regime(generalized) Kadomtsev-Petviashvili equation(generalized) Korteweg-de Vries equationweakly transverse Boussinesq system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Spectral approach to Korteweg-de Vries equations on the compactified real line ⋮ The sine-Gordon regime of the Landau-Lifshitz equation with a strong easy-plane anisotropy ⋮ Recent results for the Landau-Lifshitz equation ⋮ Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d ⋮ The KP limit of a reduced quantum Euler–Poisson equation ⋮ Rarefaction pulses for the nonlinear Schrödinger equation in the transonic limit ⋮ The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy ⋮ Long wave limit for Schrödinger maps

Cites Work

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• The Cauchy problem on large time for surface waves Boussinesq systems
• Global existence and collisions for symmetric configurations of nearly parallel vortex filaments
• Geometric optics and boundary layers for nonlinear-Schrödinger equations
• On the KPI transonic limit of two-dimensional Gross-Pitaevskii travelling waves
• Schrödinger maps and anti-ferromagnetic chains
• On the linear wave regime of the Gross-Pitaevskii equation
• Supercritical geometric optics for nonlinear Schrödinger equations
• Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
• Stability and evolution of the quiescent and travelling solitonic bubbles
• Solitary waves of generalized Kadomtsev-Petviashvili equations
• Consistency of the KP approximation
• Local Schrödinger flow into Kähler manifolds
• Secular growth estimates for hyperbolic systems.
• On the continuous limit for a system of classical spins
• Asymptotics for symmetric hyperbolic systems with a large parameter
• Justification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems
• Long wave limit for Schrödinger maps
• Rarefaction pulses for the nonlinear Schrödinger equation in the transonic limit
• Schrödinger group on Zhidkov spaces
• Topology and dynamics in ferromagnetic media
• Intermediate long wave systems for internal waves
• Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension one
• The KdV/KP-I Limit of the Nonlinear Schrödinger Equation
• THE LONG WAVE LIMIT FOR A GENERAL CLASS OF 2DQUASILINEAR HYPERBOLIC PROBLEMS
• Weakly transverse Boussinesq systems and the Kadomtsev–Petviashvili approximation
• The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity
• On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II
• On equations of KP-type
• Semitopological solitons in planar ferromagnets
• Semiclassical limit of the nonlinear Schrödinger equation in small time
• Vortex dynamics in two-dimensional antiferromagnets
• Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence
• KP lumps in ferromagnets: a three-dimensional KdV Burgers model
• Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
• Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross–Pitaevskii equation
• On the Korteweg-de Vries Long-Wave Approximation of the Gross-Pitaevskii Equation I
• On the well-posedness for the Euler-Korteweg model in several space dimensions
• Wave-type dynamics in ferromagnetic thin films and the motion of Néel walls
• Existence and properties of travelling waves for the Gross-Pitaevskii equation
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
• Quantized vortex dynamics and superfluid turbulence
• Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension two