Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear Smoothing for the Periodic Generalized Non-linear
  Schr\"odinger Equation   We consider the periodic non-linear Schr\"odinger equation with non-linearity
given by $|u|^{p-1}u$ for odd $p > 1$ in dimension $1$. We first establish that
the difference between the non-linear evolution and a phase rotation of the the
linear evolution is in a smoother space. We then study forced and damped
defocusing non-linear Schr\"odinger equations of the above type and establish
an analogous smoothing statement that extends globally in time. As a corollary
we establish both existence and smootheness for global attractors in the energy
space.

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The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th