Numerical Study of Quantized Vortex Interactions in the Nonlinear Schrödinger Equation on Bounded Domains

@article{Bao2014NumericalSO,
  title={Numerical Study of Quantized Vortex Interactions in the Nonlinear Schr{\"o}dinger Equation on Bounded Domains},
  author={Weizhu Bao and Qinglin Tang},
  journal={Multiscale Model. Simul.},
  year={2014},
  volume={12},
  pages={411-439}
}
In this paper, we study numerically quantized vortex dynamics and their interactions in the two-dimensional (2D) nonlinear Schrodinger equation (NLSE) with a dimensionless parameter $\varepsilon>0$ proportional to the size of the vortex core on bounded domains under either a Dirichlet or a homogeneous Neumann boundary condition (BC). We begin with a review of the reduced dynamical laws for time evolution of quantized vortex centers and show how to solve these nonlinear ordinary differential… 
Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law
We study analytically and numerically stability and interaction patterns of quantized vortex lattices governed by the reduced dynamical lawa system of ordinary differential equations (ODEs) - in
On the Rotating Nonlinear Klein-Gordon Equation: NonRelativistic Limit and Numerical Methods
TLDR
It is formally show that in the non-relativistic limit RKG converges to coupled rotating nonlinear Schrodinger equations (RNLS), which is used to describe the particle-antiparticle pair dynamics.
Instability of the finite‐difference split‐step method applied to the nonlinear Schrödinger equation. I. standing soliton
We consider numerical instability that can be observed in simulations of solitons of the nonlinear Schrödinger equation (NLS) by a split‐step method (SSM) where the linear part of the evolution is
Instability of the finite‐difference split‐step method applied to the nonlinear Schrödinger equation. II. moving soliton
We analyze a mechanism and features of a numerical instability (NI) that can be observed in simulations of moving solitons of the nonlinear Schrödinger equation (NLS). This NI is completely different
Modulation equations approach for solving vortex and radiation in nonlinear Schrodinger equation
We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schrodinger equation. The full modulation equations which describe the dynamics of the
Error Estimates of Local Energy Regularization for the Logarithmic Schrodinger Equation
TLDR
A local energy regularization (LER) for the LogSE is proposed by first regularizing F (ρ) = ρ ln ρ − ρ locally near ρ = 0 with a polynomial approximation in the energy functional of the Log SE and then obtaining an energy regularized logarithmic Schrödinger equation (ERLogSE) via energy variation.
An inverse problem from condensed matter physics
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross–Pitaevskii equation. At leading order, the
...
...

References

SHOWING 1-10 OF 60 REFERENCES
Numerical Study of Quantized Vortex Interaction in the Ginzburg-Landau Equation on Bounded Domains
In this paper, we study numerically quantized vortex dynamics and their interaction in the two-dimensional (2D) Ginzburg-Landau equation (GLE) with a dimensionless parameter e > 0 on bounded domains
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
The rich dynamics of quantized vortices governed by the Ginzburg-Landau-Schrödinger equation (GLSE) is an interesting problem studied in many application fields. Although recent mathematical analysis
On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation
Abstract:The nonlinear Schrödinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical
The Dynamics and Interaction of Quantized Vortices in the Ginzburg-Landau-Schrödinger Equation
TLDR
The dynamic laws of quantized vortex interactions in the Ginzburg–Landau–Schrodinger equation (GLSE) are analytically and numerically studied and the vortex motion under an inhomogeneous potential in the GLSE is studied.
A unified approach to vortex motion laws of complex scalar field equations
In this short note, we give a unified rigorous derivation of vortex motion laws of nonlinear wave (NLW) and nonlinear heat (NLH) equations based on the fluid dynamic approach the authors recently
Vortices in complex scalar fields
  • J. Neu
  • Mathematics, Physics
  • 1990
Numerical Methods for the Nonlinear Schrödinger Equation with Nonzero Far-field Conditions
  • W. Bao
  • Mathematics, Physics
  • 2004
In this paper we present numerical methods for the nonlinear Schrödinger equations (NLS) in the semiclassical regimes: iε uεt = − ε 2 ∆u + V (x)u + f(|u|)u, x ∈ R, with nonzero far-field conditions.
Vortex interaction dynamics in trapped Bose-Einstein condensates
Motivated by recent experiments studying the dynamics of configurations bearing a small number of vortices in atomic Bose-Einstein condensates (BECs), we illustrate that such systems can be
Dynamics of vortices in weakly interacting Bose-Einstein condensates
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different
Few-Particle Vortex Cluster Equilibria in Bose-Einstein Condensates: Existence and Stability
Motivated by recent experimental and theoretical studies of few-particle vortex clusters in Bose–Einstein condensates, we consider the ordinary differential equations of motion and systematically
...
...