Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soliton-phonon scattering problem in 1D nonlinear Schr\"odinger systems
  with general nonlinearity   A scattering problem (or more precisely, a transmission-reflection problem)
of linearized excitations in the presence of a dark soliton is considered in a
one-dimensional nonlinear Schr\"odinger system with a general nonlinearity: $
\mathrm{i}\partial_t \phi = -\partial_x^2 \phi + F(|\phi|^2)\phi $. If the
system is interpreted as a Bose-Einstein condensate, the linearized excitation
is a Bogoliubov phonon, and the linearized equation is the Bogoliubov equation.
We exactly prove that the perfect transmission of the zero-energy phonon is
suppressed at a critical state determined by Barashenkov's stability criterion
[Phys. Rev. Lett. 77, (1996) 1193.], and near the critical state, the
energy-dependence of the reflection coefficient shows a saddle-node type
scaling law. The analytical results are well supported by numerical calculation
for cubic-quintic nonlinearity. Our result gives an exact example of scaling
laws of saddle-node bifurcation in time-reversible Hamiltonian systems. As a
by-product of the proof, we also give all exact zero-energy solutions of the
Bogoliubov equation and their finite energy extension.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn