Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Schlesinger Deformations of Ordinary Differential Equations with
  Rational Coefficients   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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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph