Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soliton solutions of the nonlinear Schr\"odinger equation with defect
  conditions   A recent development in the derivation of soliton solutions for
initial-boundary value problems through Darboux transformations, motivated to
reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two
half-lines connected via integrable defect conditions. Thereby, the Darboux
transformation to construct soliton solutions is applied, while preserving the
spectral boundary constraint with a time-dependent defect matrix. In this
particular model, $N$-soliton solutions vanishing at infinity are constructed.
Further, it is proven that solitons are transmitted through the defect
independently of one another.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess