Related papers: Stable nonlinear modes sustained by gauge fields
We write down scalar field theory and gauge theory on two-dimensional noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$ going to i) a…
In this paper we demonstrate that solitons of a simple real scalar field model that are {\it static and linearly stable} do exist when considered in a (3+1)-dimensional, spatially compact space-time background, the static Einstein universe,…
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 propose a gauge-invariant system of the Chern-Simons-Schrodinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square…
The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
We consider asymptotic stability of a small solitary wave to supercritical 1-dimensional nonlinear Schr\"{o}dinger equations $$ iu_t+u_{xx}=Vu\pm |u|^{p-1}u \quad\text{for $(x,t)\in\mathbb{R}\times\mathbb{R}$,}$$ in the energy class. This…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…
In the classical electrodynamics of point charges in vacuum, the electromagnetic field, and therefore the Lorentz force, is ill-defined at the locations of the charges. Kiessling resolved this problem by using the momentum balance between…
We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
I study stable spatial Langmuir solitons in plasma based on nonlinear radial oscillations of charged particles. I discuss two situations when a Langmuir soliton can be stable. In the former case the stability of solitons against the…
We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical solution non-expansive whenever the exact solution is…
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
We study a SU(2) gauge theory with a classical complex modulus. Introducing a chemical potential for a conserved modulus hypercharge causes it to become unstable and start condensing. We show that the modulus condensation in turn generates…
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three…
The stability conditions for coordinate gauge independent perturbations of brane-worlds are analyzed. It is shown that, these conditions lead to the Einstein-Hilbert dynamics and to a confined gauge potential, independently of models and…
We report on detailed investigation of the stability of localized modes in the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT) symmetric potential. We are particularly focusing on the case where the…
By means of variational methods and systematic numerical analysis, we demonstrate the existence of stable solitons in three-dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and…