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Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients

A. V. Kitaev
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Abstract

We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for $2\times2$ ODEs are proved. An explicit example of the general non-Schlesinger deformation of $2\times2$-matrix ODE of the Fuchsian type with 4 singular points is constructed and application of such deformations to the construction of special solutions of the corresponding Schlesinger systems is discussed. Some examples of isomonodromy and non-isomonodromy deformations of $3\times3$ matrix ODEs are considered. The latter arise as the compatibility conditions with linear ODEs with non-singlevalued coefficients.

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A. V. Kitaev. 2001-02-18. Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients. https://doi.org/10.1088/0305-4470%2F34%2F11%2F318

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