Relations between hierarchies and inverse scattering

DOI10.1080/00036819408840289zbMath0839.58031OpenAlexW1977092703MaRDI QIDQ4854495

Robert W. Carroll

Publication date: 6 December 1995

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819408840289

zbMATH Keywords

scatteringhierarchiesKP equationsdressing

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Cites Work

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• Factorization and the dressing method for the Gel'fand-Dikii hierarchy
• On the ubiquitous Gelfand-Levitan-Marčenko (GLM) equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• New features of Backlund and Darboux transformations in 2 + 1 dimensions
• Inverse spectral transform for the Ishimori equation: I. Initial value problem
• Geometry of KDV (5): Scattering from the Grassmannian viewpoint
• Inverse Spectral Transform for the Nonlinear Evolution Equation Generating the Davey-Stewartson and Ishimori Equations
• Some connections between inverse scattering and solution hierarchies
• Linear spectral problems, non-linear equations and the δ-method

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