Bounds for the nonlinear Schrödinger approximation of the Fermi–Pasta–Ulam system

DOI10.1080/00036810903277150zbMath1194.35427OpenAlexW2051063880WikidataQ58147210 ScholiaQ58147210MaRDI QIDQ3584661

Guido Schneider

Publication date: 30 August 2010

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810903277150

zbMATH Keywords

approximationenvelope equationlattice equationnormal form transformmulti-scale approximationquadratic resonance

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Theoretical approximation in context of PDEs (35A35) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (10)

Breathers in a locally resonant granular chain with precompression ⋮ NONLINEAR WAVES IN NEWTON'S CRADLE AND THE DISCRETE p-SCHRÖDINGER EQUATION ⋮ Travelling breathers and solitary waves in strongly nonlinear lattices ⋮ KP-II Approximation for a Scalar Fermi–Pasta–Ulam System on a 2D Square Lattice ⋮ Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit ⋮ Moving Modulating Pulse and Front Solutions of Permanent Form in a FPU Model with Nearest and Next-to-Nearest Neighbor Interaction ⋮ Justification of leading order quasicontinuum approximations of strongly nonlinear lattices ⋮ On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system ⋮ Approximation of Polyatomic FPU Lattices by KdV Equations ⋮ Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity

Cites Work

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• Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model
• ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
• The validity of modulation equations for extended systems with cubic nonlinearities
• The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities

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