Nonlinear Schrödinger-type equations from multiscale reduction of PDEs. I. Systematic derivation

DOI10.1063/1.1287644zbMath0972.35146OpenAlexW1968475540MaRDI QIDQ2738195

Francesco Calogero, Xiaoda Ji, Antonio Degasperis

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1287644

zbMATH Keywords

nonlinear effectsamplitude modulationsdispersive linear partmonochromatic wave solutionsreduction of nonlinear partial differential equations

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (7)

Derivation of Korteweg-de Vries flow equations from nonlinear Schrödinger equation ⋮ Abundant coherent structures of the dispersive long-wave equation in \((2+1)\)-dimensional spaces. ⋮ Localized excitations with periodic and chaotic behaviors in \((1+1)\)-dimensional Korteweg-de Vries type system ⋮ Derivation of Korteweg‐de Vries flow equations from fourth order nonlinear Schrödinger equation ⋮ Peakon, compacton and loop excitations with periodic behavior in KdV type models related to Schrödinger system ⋮ Nonlinear Schrödinger-type equations from multiscale reduction of PDEs. II. Necessary conditions of integrability for real PDEs ⋮ Multiscale Expansion and Integrability of Dispersive Wave Equations

Cites Work

• To the integrability of the system of two coupled nonlinear Schrödinger equations
• Multiple-scale perturbation beyond the nonlinear Schrödinger equation. I
• Formation and Interaction of Sonic-Langmuir Solitons: Inverse Scattering Method
• Universal C-integrable nonlinear partial differential equation in N+1 dimensions
• Nonlinear evolution equations, rescalings, model PDEs and their integrability: II

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