Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Purely nonlinear disorder-induced localizations and their parametric
  amplification   We investigate spatial localization in a quadratic nonlinear medium in the
presence of randomness. By means of numerical simulations and theoretical
analyses we show that, in the down conversion regime, the transverse random
modulation of the nonlinear susceptibility generates localizations of the
fundamental wave that grow exponentially in propagation. The localization
length is optically controlled by the pump intensity which determines the
amplification rate. The results also apply to cubic nonlinearities.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat