Related papers: The Lugiato-Lefever equation driven by a double ti…
Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but…
We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self- focusing or defocusing nonlinearity, losses,…
We introduce a model of a passive optical cavity based on a novel variety of the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5,…
The damped driven nonlinear Schr\"odinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyper-parametric oscillators in anomalous-dispersion…
We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weakly or strongly localized) pump. The LLE is derived,…
We introduce a new equation that describes the spatio-temporal evolution of arbitrary pulses propagating in a fiber-ring cavity. This model is a significant extension of the traditionally used Lugiato-Lefever model. We demonstrate…
We introduce a discrete lossy system, into which a double hot spot (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic…
We analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while…
The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schr\"odinger equation. It is a mathematical model describing complex phenomena in dissipative and nonlinear optical cavities. Within the last two…
The interplay of periodic driving and dissipation is a fundamental feature of nonequilibrium physics. We elaborate a scenario for the formation of dissipative multi-spot excitations (MSEs) in Kerr cavities, modeled by the one- and…
We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order…
We study the gravity-driven flow of two fluid phases in a one-dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken into account. In the hyperbolic limit,…
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a…
We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain…
We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator…
We consider the renormalisation group flow of Higgs and Yukawa couplings within the simplest non--supersymmetric two Higgs doublet extension of the Standard Model (SM). In this model the couplings are adjusted so that the multiple point…
Localized dissipative structures (LDS) have been predicted to display a rich array of instabilities, yet systematic experimental studies have remained scarce. We have used a synchronously-driven optical fiber ring resonator to…
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and…
We consider a condensate of ultra cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump is making different angles with the direction of the cavity axis. We show such configuration allows a…
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) with increasing attraction, in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the…