Related papers: Longtime behavior of coupled wave equations for se…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…
In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid…
The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
The three goals of this PhD thesis are to improve the understanding of the mechanisms underlying the dynamical instabilities observed in semiconductor lasers subject to external optical feedback, to propose a technique to suppress these…
Dynamics of external cavity semiconductor lasers is known to be a complex and uncontrollable phenomenon. Due to the lack of experimental studies on the nature of the external cavity semiconductor lasers, there is a need to theoretically…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We investigate the nonlinear interaction between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of the electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the…
We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…
Optically-coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We…
We investigate the dynamic mechanisms for low frequency fluctuations in semiconductor lasers subject to delayed optical feedback, using the Lang-Kobayashi model. This system of delay differential equations displays pronounced envelope…