Monodromy preserving deformation of linear ordinary differential equations with rational coefficients : I. General theory and τ-function
1981Citations per year
Abstract: (Elsevier B.V.)
A general theory of monodromy preserving deformation is developed for a system of linear ordinary differential equations
, 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 d
ω=0 for each solution of the deformation equations. Examples corresponding to the “soliton” and “rational” solutions are discussed.References(32)
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