Finite-dimensional Sturm-Liouville vessels and their tau functions

DOI10.1007/s00020-011-1899-7zbMath1259.47014OpenAlexW1969656070MaRDI QIDQ429734

Andrey Melnikov

Publication date: 20 June 2012

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-011-1899-7

zbMATH Keywords

nonlinear differential equationsBäcklund transformationsfinite-dimensional vessels

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Sturm-Liouville theory (34B24) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

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Representations of Lie algebras by non-skewselfadjoint operators in Hilbert space ⋮ Solution of the Korteweg-de Vries equation on the line with analytic initial potential ⋮ Differential algebras with Banach-algebra coefficients. I: From \(C^*\)-algebras to the \(K\)-theory of the spectral curve ⋮ Schur algorithm in the class \({\mathcal{SI}}\) of \(J\)-contractive functions intertwining solutions of linear differential equations ⋮ Classification of KdV vessels with constant parameters and two dimensional outer space ⋮ Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrant ⋮ On construction of solutions of evolutionary nonlinear Schrödinger equation ⋮ Null/pole interpolation problem in the class \(\mathcal {RI}\) of rational functions intertwining solutions of linear differential equations ⋮ Solution of the Boussinesq equation using evolutionary vessels ⋮ Inverse scattering of canonical systems and their evolution

Cites Work

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• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• A Schur algorithm for transfer function of over-determined conservative systems, invariant in one direction
• Connection colligations on Hilbert bundles
• Schur algorithm in the class \({\mathcal{SI}}\) of \(J\)-contractive functions intertwining solutions of linear differential equations
• The Inverse Problem in the Quantum Theory of Scattering
• Computing the Galois group of a linear differential equation
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

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