Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbounded Sobolev trajectories and modified scattering theory for a wave
  guide nonlinear Schr\"odinger equation   We consider the following wave guide nonlinear Schr\"odinger equation,
\begin{equation} (i\partial \_t+\partial \_{xx}-\vert D\_y\vert )U=\vert U\vert
^2U\ \tag{WS} \end{equation} on the spatial cylinder $\mathbb{R} \_x\times
\mathbb{T} \_y$. We establish a modified scattering theory between small
solutions to this equation and small solutions to the cubic Szeg\H{o} equation.
The proof is an adaptation of the method of
Hani--Pausader--Tzvetkov--Visciglia. Combining this scattering theory with a
recent result by G\'erard--Grellier, we infer existence of global solutions to
(WS) which are unbounded in the space $L^2\_xH^s\_y(\mathbb{R} \times
\mathbb{T} )$ for every $s\textgreater{}\frac 12$.

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th