Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine Lie group approach to a derivative nonlinear Schr\"odinger
  equatoin and its similarity reduction   The generalized Drinfel'd-Sokolov hierarchies studied by de
Groot-Hollowood-Miramontes are extended from the viewpoint of Sato-Wilson
dressing method. In the A_1^(1) case, we obtain the hierarchy that include the
derivative nonlinear Schr\"odinger equation. We give two types of affine Weyl
group symmetry of the hierarchy based on the Gauss decomposition of the A_1^(1)
affine Lie group. The fourth Painlev\'e equation and their Weyl group symmetry
are obtained as a similarity reduction. We also clarify the connection between
these systems and monodromy preserving deformations.

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The categories of this paper are: atom-ph
2
The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con