Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational approximations of soliton dynamics in the
  Ablowitz-Musslimani nonlinear Schr\"odinger equation   We study the integrable nonlocal nonlinear Schr\"odinger equation proposed by
Ablowitz and Musslimani, that is considered as a particular example of
equations with parity-time ($\mathcal{PT}$) symmetric self-induced potential.
We consider dynamics (including collisions) of moving solitons. Analytically we
develop a collective coordinate approach based on variational methods and
examine its applicability in the system. We show numerically that a single
moving soliton can pass the origin and decay or be trapped at the origin and
blows up at a finite time. Using a standard soliton ansatz, the variational
approximation can capture the dynamics well, including the finite-time blow up,
even though the ansatz is relatively far from the actual blowing-up soliton
solution. In the case of two solitons moving towards each other, we show that
there can be a mass transfer between them, in addition to wave scattering. We
also demonstrate that defocusing nonlinearity can support bright solitons.

2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph