Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex Operators and Solitons of Constrained KP Hierarchies   We construct the vertex operator representation for the Affine Kac-Moody
$SL(M+K+1)$ algebra, which is relevant for the construction of the soliton
solutions of the constrained KP hierarchies. The oscillators involved in the
vertex operator construction are provided by the Heisenberg subalgebras of
$SL(M+K+1)$ realized in the unconventional gradations. The well-known limiting
cases are the homogeneous Heisenberg subalgebra of $SL(M+1)$ and the principal
Heisenberg subalgebra of ${\hat{sl}}(K+1)$. The explicit example of $M=K=1$ is
discussed in detail and the corresponding soliton solutions and tau-functions
are given.

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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
4
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: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph