Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Schr\"odinger equation with singular potentials   We study the Cauchy problem for the non-linear Schr\"odinger equation with
singular potentials. For point-mass potential and nonperiodic case, we prove
existence and asymptotic stability of global solutions in weak-L^{p} spaces.
Specific interest is give to the point-like $\delta$ and $\delta'$ impurity and
for two $\delta$-interactions in one dimension. We also consider the periodic
case which is analyzed in a functional space based on Fourier transform and
local-in-time well-posedness is proved.

33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs