Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot soliton solutions for the one-dimensional non-linear
  Schr\"{o}dinger equation   We identify that for a broad range of parameters a variant of the soliton
solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it
breather}, is distinct when one studies the associated space curve (or soliton
surface), which in this case is knotted. The signi ficance of these solutions
with such a hidden non-trivial topological element is pre-eminent on two
counts: it is a one-dimensional model, and the no nlinear Schr\"{o}dinger
equation is well known as a model for a variety of physical systems.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th