Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schrodinger-Helmholtz Equation as Numerical Regularization of
  the Nonlinear Schrodinger Equation   A regularized $\alpha-$system of the Nonlinear Schr\"{o}dinger Equation (NLS)
with $2\sigma$ nonlinear power in dimension $N$ is studied. We prove existence
and uniqueness of local solution in the case $1 \le \sigma <\frac{4}{N-2}$ and
existence and uniqueness of global solution in the case $1 \le \sigma <
\frac{4}{N}$. When $\alpha \to 0^+$, this regularized system will converge to
the classical NLS in the appropriate range. In particular, the purpose of this
numerical regularization is to shed light on the profile of the blow up
solutions of the original Nonlinear Schr\"{o}dinger Equation in the range
$\frac{2}{N}\le \sigma <\frac{4}{N}$, and in particular for the critical case
$\sigma = \frac{2}{N}$.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat