Integrable systems and isomonodromy deformations

DOI10.1016/0167-2789(93)90003-JzbMath0795.35077arXivsolv-int/9801010OpenAlexW2002925522MaRDI QIDQ2367672

David H. Sattinger, Richard W. Beals

Publication date: 18 August 1993

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

Full work available at URL: https://arxiv.org/abs/solv-int/9801010

zbMATH Keywords

Painlevé propertyAKNS hierarchiesequation of DouglasGel'fand- Dikij hierarchies

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (6)

Factorization and the dressing method for the Gel'fand-Dikii hierarchy ⋮ Deformation analysis of matrix models ⋮ The sixth Painlevé equation as similarity reduction of \({\widehat{\mathfrak{gl}}_3}\) generalized Drinfel'd-Sokolov hierarchy ⋮ Duality for the general isomonodromy problem ⋮ On the Riemann-Hilbert-Birkhoff inverse monodromy problem associated with the third Painlevé equation ⋮ On the Riemann--Hilbert--Birkhoff inverse monodromy problem and the Painlevé equations

Cites Work

• Unnamed Item
• Unnamed Item
• Strings in less than one dimension and the generalized KdV hierarchies
• Geometry of the string equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Multiphase similarity solutions of integrable evolution equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III
• The isomonodromic deformation method in the theory of Painlevé equations
• Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
• Monodromy- and spectrum-preserving deformations. I
• Differential equations with polynomial coefficients
• Scattering and inverse scattering for first order systems
• Hamiltonian Hierarchies on Semisimple Lie Algebras
• The inverse scattering transform: Semi-infinite interval
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Rational Solutions of Painlevé Equations

This page was built for publication: Integrable systems and isomonodromy deformations