Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First principles derivation of NLS equation for BEC with cubic and
  quintic nonlinearities at non zero temperature. Dispersion of linear waves   In this work we presented a derivation of the quantum hydrodynamic equations
for neutral bosons. We considered short range interaction between particles.
This interaction consist binary interaction $U(\textbf{r}_{i},\textbf{r}_{j})$
and three particle interaction
$U(\textbf{r}_{i},\textbf{r}_{j},\textbf{r}_{k})$, the last one does not
include binary interaction between particles. From the quantum hydrodynamic
(QHD) equations for Bose-Einstein condensate we derive nonlinear
Schr\"{o}dinger equation. This equation includes the nonlinearities of third
and fifth degree. It is at zero temperature. Explicit form of the constant of
three-particle interaction was taken. First of all, developed method we used
for studying of dispersion of linear waves. Dispersion characteristics of
linear waves were compared for the cases. It were of two-particle interaction
in approximation third order to interaction radius (TOIR) and three-particle
interaction, at zero temperature. We consider influence of temperature on
dispersion of elementary excitations. For this aim we derive a system of QHD
equations at non-zero temperature. Obtained system of equation is an analog of
well-known two-fluid hydrodynamics. Moreover, it is generalization of two-fluid
hydrodynamics equations due to three-particle interaction. Evident expressions
of the velocities of the first and second sound via the concentrations of
superfluid and noncondesate components is calculated.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas