Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of the Nonlinear Schrodinger Equation with Prescribed
  Asymptotics at Infinity   We prove local existence and uniqueness of solutions for the one-dimensional
nonlinear Schr\"odinger (NLS) equations $iu_t + u_{xx} \pm |u|^2 u = 0$ in
classes of smooth functions that admit an asymptotic expansion at infinity in
decreasing powers of $x$. We show that an asymptotic solution differs from a
genuine solution by a Schwartz class function which solves a generalized
version of the NLS equation. The latter equation is solved by discretization
methods. The proofs closely follow previous work done by the author and others
on the Korteweg-De Vries (KdV) equation and the modified KdV equations.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol