Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth Bound and Nonlinear Smoothing for the Periodic Derivative
  Nonlinear Schr\"odinger Equation   A polynomial-in-time growth bound is established for global Sobolev
$H^s(\mathbb T)$ solutions to the derivative nonlinear Schr\"odinger equation
on the circle with $s>1$. These bounds are derived as a consequence of a
nonlinear smoothing effect for an appropriate gauge-transformed version of the
periodic Cauchy problem, according to which a solution with its linear part
removed possesses higher spatial regularity than the initial datum associated
with that solution.

24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph