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.

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

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

M3 - Article

AN - SCOPUS:49149137872

SN - 0167-2789

VL - 2

SP - 306

EP - 352

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 2

ER -