### 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 language | English |
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Pages (from-to) | 306-352 |

Number of pages | 47 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 2 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1981 |

Externally published | Yes |

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

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## Cite this

Jimbo, M., Miwa, T., & Ueno, K. (1981). Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and τ-function.

*Physica D: Nonlinear Phenomena*,*2*(2), 306-352. https://doi.org/10.1016/0167-2789(81)90013-0