Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained KP Hierarchies: Additional Symmetries, Darboux-B\"{a}cklund
  Solutions and Relations to Multi-Matrix Models   This paper provides a systematic description of the interplay between a
specific class of reductions denoted as \cKPrm ($r,m \geq 1$) of the primary
continuum integrable system -- the Kadomtsev-Petviashvili ({\sf KP}) hierarchy
and discrete multi-matrix models. The relevant integrable \cKPrm structure is a
generalization of the familiar $r$-reduction of the full {\sf KP} hierarchy to
the $SL(r)$ generalized KdV hierarchy ${\sf cKP}_{r,0}$. The important feature
of \cKPrm hierarchies is the presence of a discrete symmetry structure
generated by successive Darboux-B\"{a}cklund (DB) transformations. This
symmetry allows for expressing the relevant tau-functions as Wronskians within
a formalism which realizes the tau-functions as DB orbits of simple initial
solutions. In particular, it is shown that any DB orbit of a ${\sf cKP}_{r,1}$
defines a generalized 2-dimensional Toda lattice structure. Furthermore, we
consider the class of truncated {\sf KP} hierarchies ({\sl i.e.}, those defined
via Wilson-Sato dressing operator with a finite truncated pseudo-differential
series) and establish explicitly their close relationship with DB orbits of
\cKPrm hierarchies. This construction is relevant for finding partition
functions of the discrete multi-matrix models.
  The next important step involves the reformulation of the familiar
non-isospectral additional symmetries of the full {\sf KP} hierarchy so that
their action on \cKPrm hierarchies becomes consistent with the constraints of
the reduction. Moreover, we show that the correct modified additional
symmetries are compatible with the discrete DB symmetry on the \cKPrm DB
orbits.
  The above technical arsenal is subsequently applied to obtain complete

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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics