Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On existence of global solutions of the one-dimensional cubic NLS for
  initial data in the modulation space $M_{p,q}(\mathbb R)$   We prove global existence for the one-dimensional cubic non-linear
Schr\"odinger equation in modulation spaces $M_{p,p'}$ for $p$ sufficiently
close to $2$. In contrast to known results, our result requires no smallness
condition on initial data. The proof adapts a splitting method inspired by work
of Vargas-Vega and Hyakuna-Tsutsumi to the modulation space setting and
exploits polynomial growth of the free Schr\"odinger group on modulation
spaces.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex