### 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 |

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### 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.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 2, no. 2, pp. 306-352. https://doi.org/10.1016/0167-2789(81)90013-0

}

TY - JOUR

T1 - Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and τ-function

AU - Jimbo, Michio

AU - Miwa, Tetsuji

AU - Ueno, Kimio

PY - 1981

Y1 - 1981

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49149137872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149137872&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(81)90013-0

DO - 10.1016/0167-2789(81)90013-0

M3 - Article

VL - 2

SP - 306

EP - 352

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2

ER -