On generating functions in the AKNS hierarchy

DOI10.1016/S0375-9601(02)00935-0zbMath0997.37049arXivnlin/0208025OpenAlexW2169394788MaRDI QIDQ1612838

A. M. Kamchatnov, Maxim P. Pavlov

Publication date: 4 September 2002

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0208025

zbMATH Keywords

stimulated Raman scatteringmutual commutativityself-induced transparency equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (9)

A vectorial binary Darboux transformation for the first member of the negative part of the AKNS hierarchy ⋮ An integrable lattice equation related to the nKN system ⋮ Negative flows for several integrable models ⋮ Liouville integrability and explicit solutions for a Frobenius‐coupled integrable lattice hierarchy ⋮ Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation ⋮ On generating equations for the Kaup-Newell hierarchy ⋮ The four-dimensional Martínez Alonso-Shabat equation: reductions and nonlocal symmetries ⋮ An alternative approach to solve the mixed AKNS equations ⋮ NLS-type equations from quadratic pencil of Lax operators: negative flows

Cites Work

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• Solitons in stimulated Raman scattering and resonant two-photon propagation
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Fredholm determinants and the mKdV/Sinh-Gordon hierarchies
• Boundary value problems compatible with symmetries
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Tau-functions and dressing transformations for zero-curvature affine integrable equations
• The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy
• Unified approach to strings and vortices with soliton solutions

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