Related papers: Linearized dynamic stability for vortices of Ginzb…
The initial value problem for the Ginzburg-Landau-Schr\"odinger equation is examined in the $\epsilon \rightarrow 0$ limit under two main assumptions on the initial data $\phi^\epsilon$. The first assumption is that $\phi^\epsilon$ exhibits…
Since the Ginzburg-Landau theory is concerned with macroscopic phenomena, and gravity affects how objects interact at the macroscopic level. It becomes relevant to study the Ginzburg-Landau theory in curved space, that is, in the presence…
Using a combination of the variation approximation (VA) and direct simulations, we consider the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a…
The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
We study spectral instability of steady states to the linearized 2D Euler equations on the torus written in vorticity form via certain Birman-Schwinger type operators $K_{\lambda}(\mu)$ and their associated 2-modified perturbation…
We consider the linear stability to axisymmetric perturbations of the family of inviscid vortex rings discovered by Norbury (1973). Since these vortex rings are obtained as solutions to a free-boundary problem, their stability analysis is…
In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability…
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing…
We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a…
This paper studies questions related to the dynamic transition between local and global minimizers in the Ginzburg-Landau theory of superconductivity. We derive a heuristic equation governing the dynamics of vortices that are close to the…
We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have…
We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a…
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong…
We study solutions of the 2D Ginzburg-Landau equation -\Delta u+\frac{1}{\ve^2}u(|u|^2-1)=0 subject to "semi-stiff" boundary conditions: the Dirichlet condition for the modulus, |u|=1, and the homogeneous Neumann condition for the phase.…
We numerically study the symmetry breaking instabilities of vortex patterns in a rotating harmonic potential using a type of Ginzburg-Landau equation. The configurations of vortex lattices change markedly by the symmetry-breaking…
By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected…
We present numerical studies of the dynamics of vortices in the Ginzburg Landau model using equations derived from the gradient flow of the free energy. These equations have previously been proposed to describe the dynamics of n-vortices…