Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries and reductions on the noncommutative Kadomtsev-Petviashvili
  and Gelfand-Dickey hierarchies   In this paper, we construct the additional flows of the noncommutative
Kadomtsev-Petviashvili(KP) hierarchy and the additional symmetry flows
constitute an infinite dimensional Lie algebra $W_{1+\infty}$. In addition, the
generating function of the additional symmetries can also be proved to have a
nice form in terms of wave functions and this generating symmetry is used to
construct the noncommutative KP hierarchy with self-consistent sources and the
constrained noncommutative KP hierarchy. The above results will be further
generalized to the noncommutative Gelfand-Dickey hierarchies which contains
many interesting noncommutative integrable systems such as the noncommutative
KdV hierarchy and noncommutative Boussinesq hierarchy. Meanwhile, we construct
two new noncommutative systems including odd noncommutative C type
Gelfand-Dickey and even noncommutative C type Gelfand-Dickey hierarchies. Also
using the symmetry, we can construct a new noncommutative Gelfand-Dickey
hierarchy with self-consistent sources. Basing on the natural differential Lax
operator of the noncommutative Gelfand-Dickey hierarchy, the string equations
of the noncommutative Gelfand-Dickey hierarchy are also derived.

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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
1
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: acc-phys
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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph