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

Michio Jimbo*, Tetsuji Miwa, Kimio Ueno

*この研究の対応する著者

研究成果: Article査読

489 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)306-352
ページ数47
ジャーナルPhysica D: Nonlinear Phenomena
2
2
DOI
出版ステータスPublished - 1981
外部発表はい

ASJC Scopus subject areas

  • 応用数学
  • 統計物理学および非線形物理学

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