On the nonlinear Schrödinger limit of the Korteweg-de Vries equation

DOI10.1016/0167-2789(88)90088-7zbMath0697.35125OpenAlexW2247598902MaRDI QIDQ910961

N. E. Zubov

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0167-2789(88)90088-7

zbMATH Keywords

Korteweg-de Vries equationnonlinear Schrödinger limit

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Nonlinear analysis and solitary waves for two superposed streaming electrified fluids of uniform depths with rigid boundaries ⋮ Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform \(\mu\)-representation ⋮ Interaction of two quasi-monochromatic waves in shallow water ⋮ The shallow-water nonlinear Schrödinger equation in Lagrangian coordinates ⋮ A discrete multiple scales analysis of a discrete version of the Korteweg-de Vries equation ⋮ Computation of the direct scattering transform for the nonlinear Schrödinger equation ⋮ Justification of the NLS approximation for the KdV equation using the Miura transformation ⋮ Weakly nonlinear wavepackets in the Korteweg-de Vries equation: The KdV/NLS connection ⋮ Nonlinear Fourier analysis for the infinite-interval Korteweg-de Vries equation. I: An algorithm for the direct scattering transform

Cites Work

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• Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation
• Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• The Periodic Cubic Schrõdinger Equation
• The inverse scattering transform: Semi-infinite interval
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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