Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients
نویسنده
چکیده
We consider deformations of 2×2 and 3×3 matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don’t satisfy the wellknown system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for 2× 2 ODEs are proved. An explicit example of the general non-Schlesinger deformation of 2×2-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 3×3 matrix ODEs are considered. The latter arise as the compatibility conditions with linear ODEs with non-singlevalued coefficients. 2000 Mathematics Subject Classification: 34A20, 34E20, 33E30. Short title: Non-Schlesinger Isomonodromy Deformations ∗E-mail: [email protected]
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