Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and τ-function

Michio Jimbo, Tetsuji Miwa, Kimio Ueno

Research output: Contribution to journalArticle

430 Citations (Scopus)

Abstract

A general theory of monodromy preserving deformation is developed for a system of linear ordinary differential equations dY dx=A(x)Y, where A(x) is a rational matrix. The non-linear deformation equations are derived and their complete integrability is proved. An explicit formula is found for a 1-form ω, expressed rationally in terms of the coefficients of A(x), that has the property dω=0 for each solution of the deformation equations. Examples corresponding to the "soliton" and "rational" solutions are discussed.

Original languageEnglish
Pages (from-to)306-352
Number of pages47
JournalPhysica D: Nonlinear Phenomena
Volume2
Issue number2
DOIs
Publication statusPublished - 1981
Externally publishedYes

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Linear Ordinary Differential Equations
Monodromy
Ordinary differential equations
preserving
differential equations
Coefficient
coefficients
Complete Integrability
Rational Solutions
Solitons
Explicit Formula
solitary waves
matrices

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and τ-function. / Jimbo, Michio; Miwa, Tetsuji; Ueno, Kimio.

In: Physica D: Nonlinear Phenomena, Vol. 2, No. 2, 1981, p. 306-352.

Research output: Contribution to journalArticle

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