Factorization and the dressing method for the Gel'fand-Dikii hierarchy

DOI10.1016/0167-2789(93)90247-XzbMath0770.34060arXivsolv-int/9801011OpenAlexW1989762844MaRDI QIDQ2366476

David H. Sattinger, Jacek Szmigielski

Publication date: 29 June 1993

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

Full work available at URL: https://arxiv.org/abs/solv-int/9801011

zbMATH Keywords

Baker-Akhiezer functiondressing methodisospectral flowspotential flows\(n\)th order linear scalar differential operatorAdler-Kostant-Symes methodGel'fand- Dikii flowsLie algebra decompositionsmatrix Riemann-Hilbert factorizationsscattering class

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (7)

The Riemann problem and matrix-valued potentials with a convergent Baker-Akhiezer function ⋮ Holomorphic solutions of soliton equations ⋮ Relations between hierarchies and inverse scattering ⋮ Central affine curve flow on the plane ⋮ Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies ⋮ On holomorphic solutions of equations of Korteweg–de Vries type ⋮ Remarks on the local version of the inverse scattering method

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• Systems of integral equations on a half line with kernels depending on the difference of arguments
• Direct and inverse scattering on the line with arbitrary singularities
• The Inverse Problem for Ordinary Differential Operators on the Line
• Infinite-dimensional homogeneous manifolds with translational symmetry and nonlinear partial differential equations

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