Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Study of Quantized Vortex Interaction in Complex
  Ginzburg--Landau Equation on Bounded Domains   In this paper, we study numerically quantized vortex dynamics and their
interaction in the two-dimensional complex Ginzburg-Landau equation (CGLE) with
a dimensionless parameter $\vep>0$ on bounded domains under either Dirichlet or
homogeneous Neumann boundary condition. We begin with a review of the reduced
dynamical laws (RDLs) for time evolution of quantized vortex centers in CGLE
and show how to solve these nonlinear ordinary differential equations
numerically. Then we present efficient and accurate numerical methods for
solving the CGLE on either a rectangular or a disk domain under either
Dirichlet or homogeneous Neumann boundary condition. Based on these efficient
and accurate numerical methods for CGLE and the RDLs, we explore rich and
complicated quantized vortex dynamics and interaction of CGLE with different
$\vep$ and under different initial physical setups, including single vortex,
vortex pair, vortex dipole and vortex lattice, compare them with those obtained
from the corresponding RDLs, and identify the cases where the RDLs agree
qualitatively and/or quantitatively as well as fail to agree with those from
CGLE on vortex interaction. Finally, we also obtain numerically different
patterns of the steady states for quantized vortex lattices in the CGLE
dynamics on bounded domains.

6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph