Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux Transforms for the $\hat B_{n}^{(1)}$-hierarchy   The $\hat B_n^{(1)}$-hierarchy is constructed from the standard splitting of
the affine Kac-Moody algebra $\hat B_n^{(1)}$, the Drinfeld-Sokolov $\hat
B_n^{(1)}$-KdV hierarchy is obtained by pushing down the $\hat B_n^{(1)}$-flows
along certain gauge orbit to a cross section of the gauge action. In this
paper, we
  (1) use loop group factorization to construct Darboux transforms (DTs) for
the $\hat B_n^{(1)}$-hierarchy,
  (2) give a Permutability formula and scaling transform for these DTs,
  (3) use DTs of the $\hat B_{n}^{(1)}$-hierarchy to construct DTs for the
$\hat B_n^{(1)}$-KdV and the isotropic curve flows of B-type,
  (4) give algorithm to construct soliton solutions and write down explicit
soliton solutions for the third $\hat B_1^{(1}$-KdV, $\hat B_2^{(1)}$-KdV flows
and isotropic curve flows on $\mathbb{R}^{2,1}$ and $\mathbb{R}^{3,2}$ of
B-type.

5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat