Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting and focusing of neutrino collective states   It is shown that the collective nonlinear interactions between intense
neutrino or anti-neutrino fluxes and a dense neutrino plasma are governed by a
multi-dimensional coupled cubic Schr\"odinger equation in which the interaction
potential is positive or negative depending on the neutrino type. The cubic
Schr\"odinger equation describes the splitting and focusing of intense neutrino
beams due to the nonlinear excitations associated with the modifications of the
individual neutrino energies in a dense neutrino background.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph