Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable
  System   We show that the 2-matrix string model corresponds to a coupled system of
$2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a
specific ``symmetry'' constraint. The latter together with the
Miura-Konopelchenko map for $\KPm$ are the continuum incarnation of the matrix
string equation. The $\KPm$ Miura and B\"{a}cklund transformations are natural
consequences of the underlying lattice structure. The constrained $\KPm$ system
is equivalent to a $1+1$-dimensional generalized KP-KdV hierarchy related to
graded ${\bf SL(3,1)}$. We provide an explicit representation of this
hierarchy, including the associated ${\bf W(2,1)}$-algebra of the second
Hamiltonian structure, in terms of free currents.

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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex