Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the growth of high Sobolev norms for certain one-dimensional
  Hamiltonian PDEs   This paper is devoted to the study of large time bounds for the Sobolev norms
of the solutions of the following fractional cubic Schr{\"o}dinger equation on
the torus :$$i \partial\_t u = |D|^\alpha u+|u|^2 u, \quad u(0,
\cdot)=u\_0,$$where $\alpha$ is a real parameter. We show that, apart from the
case $\alpha = 1$, which corresponds to a half-wave equation with no dispersive
property at all, solutions of this equation grow at a polynomial rate at most.
We also address the case of the cubic and quadratic half-wave equations.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics