Related papers: Linearized dynamic stability for vortices of Ginzb…
We derive the exact equation of motion for a vortex in two- and three- dimensional non-relativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the…
The work is devoted to numerical investigation of stability of stationary localized modes ("gap solitons") for the one-dimentional nonlinear Schr\"odinger equation (NLSE) with periodic potential and repulsive nonlinearity. Two classes of…
The Ginzburg-Landau equations play a key role in superconductivity and particle physics. They inspired many imitations in other areas of physics. These equations have two remarkable classes of solutions -- vortices and (Abrikosov) vortex…
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schr\"{o}dinger equation with the spatial dimension $D\geqslant 2$ with a multiplicative random term depending on the time and space coordinates. To…
We study a variational Ginzburg-Landau type model depending on a small parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to have unit length…
The dynamics and stability of continuous-wave and multi-pulse structures are studied theoretically, for a generalized model of passively mode-locked fiber laser with an arbitrary nonlinearity. The model is characterized by a complex…
We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to…
Vortex shedding is an important physical phenomenon observed across many spatial and temporal scales in fluids. Previous experimental and theoretical studies have established a hierarchy of local and global reduced-order models for vortex…
We consider a one-dimensional discrete nonlinear Schr{\"o}dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to…
The dynamical behaviors of electromagnetic (EM) solitons formed due to nonlinear interaction of linearly polarized intense laser light and relativistic degenerate plasmas are studied. In the slow motion approximation of relativistic…
Columnar vortices are stationary solutions of the three-dimensional Euler equations with axial symmetry, where the velocity field only depends on the distance to the axis and has no component in the axial direction. Stability of such flows…
Thermodynamic stability of composite vortex in a two-component superconductor is investigated by the Ginzburg-Landau theory. The predicted nature of these vortices has recently attracted much attention. Here we consider axially symmetric…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a…
In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schr{\"o}dinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the…
The aim of this work is to establish a linear instability criterium of stationary solutions for the Korteweg-de Vries model on a star graph with a structure represented by a finite collections of semi-infinite edges. By considering a…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime;…
We study, analytically and numerically, the dynamical behavior of the solutions of the complex Ginzburg-Landau equation with diffraction but without diffusion, which governs the spatial evolution of the field in an active nonlinear laser…
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…