Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soliton solutions of driven non-linear and higher order non-linear
  Schr\"odinger equations   We analyse the structure of the exact, dark and bright soliton solutions of
the driven non-linear Schr\"odinger equation. It is found that, a wide class of
solutions of the higher order non-linear Schr\"odinger equation with a source
can also be obtained through the above procedure. Distinct parameter ranges,
allowing the existence of these solutions, phase locked with their respective
sources, are delineated. Conditions for obtaining non-propagating solutions are
found to be quite different for both the equations. A special case, where the
scale of the soliton emerges as a free parameter, is obtained and the condition
under which solitons can develop singularity is pointed out. We also study the
highly restrictive structure of the localised solutions, when the phase and
amplitude get coupled.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
19
The categories of this paper are: eess