Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions to the nonlinear Schr\"odinger equation with
  time-dependent coefficients   In this paper, the trial function method is employed to find the exact
solutions for high-order nonlinear Schr\"odinger equations with time-dependent
coefficients. This system describes the propagation of ultrashort light pulses
in nonlinear fibers, with self-steepening and self-frequency shift effects. As
a result, we derive a range of exact solutions which include Jacobi elliptic
function solutions, solitary wave solutions, and rational function solutions.

31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ