Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on critical points of integrals of soliton equations   We consider the problem of extending the integrals of motion of soliton
equations to the space of all finite-gap solutions. We consider the critical
points of these integrals on the moduli space of Riemann surfaces with marked
points and jets of local coordinates. We show that the solutions of the
corresponding variational problem have an explicit description in terms of
real-normalized differentials on the spectral curve. Such conditions have
previously appeared in a number of problems of mathematical physics.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol