Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the R. Fuchs's problem for the Painlev\'e equations   In this article we consider a first-order completely integrable system of
partial differential equations $\partial \Fi/partial x=A(x, t) \Fi, \partial
\Fi/partial t=B(x, t) \Fi$ with $\Fi=(\fi_1, \fi_2)^{\tau}$ where $A(x, t)$ and
$B(x, t)$ are 2 by 2 holomorphic matrices functions. Under some assumptions we
find a variable change by which the system $\partial \Fi/\partial x=A(x, t)
\Fi$ is reduced to an equation independent on the variable $t$. As an
application we show that the R. Fuchs's conjecture for the Painlev\'e equations
is true for some algebraic solutions.

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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th