Macroscopic lattice dynamics

DOI10.1016/0167-2789(94)90035-3zbMath0814.34074OpenAlexW2053096830MaRDI QIDQ1344755

C. David Levermore, Mark H. Hays, Peter D. Miller

Publication date: 22 June 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10150/186962

zbMATH Keywords

discrete nonlinear Schrödinger equationfully nonlinear modulation equationssingle-phase harmonic wavetrainsspatially discrete nonintegrable flows

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Additive difference equations (39A10)

Related Items

The closeness of localized structures between the Ablowitz–Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems ⋮ Modulation of multiphase waves in the presence of resonance ⋮ The closeness of the Ablowitz-Ladik lattice to the discrete nonlinear Schrödinger equation ⋮ Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems ⋮ Finite genus solutions to the Ablowitz‐Ladik equations ⋮ Exact solutions of the nonlocal Hirota equations ⋮ Numerical experiments on the modulation theory for the nonlinear atomic chain ⋮ Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms ⋮ Geometric integrators for the nonlinear Schrödinger equation ⋮ Large oscillations arising in a dispersive numerical scheme ⋮ Lagrangian and Hamiltonian two-scale reduction ⋮ Dispersive shock waves in lattices: a dimension reduction approach

Cites Work

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• The discrete self-trapping equation
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• The toda shock problem
• Dispersive Regularization of the Whitham Equation for the Toda Lattice
• Nonlinear differential–difference equations and Fourier analysis
• The Evolution of Multi‐Phase Modes for Nonlinear Dispersive Waves

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