Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit form of the effective evolution equation for the randomly
  forced Schr\"{o}dinger equation with quadratic nonlinearity   An effective equation describes a weakly nonlinear wave field evolution
governed by nonlinear dispersive PDEs \emph{via} the set of its resonances in
an arbitrary big but finite domain in the Fourier space. We consider the
Schr\"{o}dinger equation with quadratic nonlinearity including small external
random forcing/dissipation.
  An effective equation is deduced explicitly for each case of monomial
quadratic nonlinearities $ u^2, \, \bar{u}u, \, \bar{u}^2$ and the sets of
resonance clusters are studied. In particular, we demonstrate that the
nonlinearity $\bar{u}^2$ generates no 3-wave resonances and its effective
equation is degenerate while in two other cases the sets of resonances are not
empty. Possible implications for wave turbulence theory are briefly discussed.

32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph