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We prove a quantitative result of convergence of a conservative stochastic particle system to the solution of the homogeneous Landau equation for hard potentials. There are two main difficulties: (i) the known stability results for this…
In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we…
We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important. Main attention is paid to linear stability analysis and numerical investigation of a…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an earlier paper by the first two authors, the solvability of the…
Near-field coupling between nanolasers enables collective high-power lasing but leads to complex spectral reshaping and multimode operation, limiting the emission brightness, spatial coherence and temporal stability. Many lasing…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T->0, the steady state is dominated by a single configuration…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. So far, nonlinear stability of such…
Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain, opening several fascinating explorations of nonlinear dynamics in mode-locked lasers. However, the…
We consider a nonlinear Schroedinger equation with a finite bands periodic potential in R . We assume the existence of an orbitally stable family of ground states. We prove that under appropriate hypotheses the ground states are…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
Period-doubling bifurcation is a universal dynamic of nonlinear systems, which has been extensively investigated in laser systems with a single transverse mode. This study presents an experimental observation and theoretical investigation…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of…