Complex Whitham deformations in problems with ``integrable instability

DOI10.1007/BF02364978zbMath0899.35105OpenAlexW3022616336MaRDI QIDQ5906844

Ramil' F. Bikbaev

Publication date: 3 February 1998

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02364978

zbMATH Keywords

focusing nonlinear Schrödinger equationWhitham deformation theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (1)

The complex MKDV equation with step-like initial data: Large time asymptotic analysis

Cites Work

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• Influence of viscosity on the structure of shock waves in the MKdV model
• ``Domain walls in the isotropic Heisenberg model
• Example of shock waves in unstable media: The focusing nonlinear Schrödinger equation
• On the parametrization of finite-gap solutions by frequency and wavenumber vectors and a theorem of I. Krichever
• The small dispersion limit of the korteweg-de vries equation. ii
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation

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