Related papers: Dynamic Models and Nonlinear Filtering of Wave Pro…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
The majority of stochastic channel models rely on the electromagnetic far-field assumption, which allows to decompose the channel in terms of plane waves. The far-field assumption breaks down in future applications that push towards the…
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
The problem of distributed or decentralized detection and estimation in applications such as wireless sensor networks has often been considered in the framework of parametric models, in which strong assumptions are made about a statistical…
The efficient deployment and operation of any wireless communication ecosystem rely on knowledge of the received signal quality over the target coverage area. This knowledge is typically acquired through radio propagation solvers, which…
We give an overview of recent developments in the modeling of radiowave propagation, based on machine learning algorithms. We identify the input and output specification and the architecture of the model as the main challenges associated…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Based on the nonlinear equations of the density wave theory, the evolutionary direction and the observable conditions on spiral galaxies may be derived by the qualitative analysis theory.
Radio propagation modeling and prediction is fundamental for modern cellular network planning and optimization. Conventional radio propagation models fall into two categories. Empirical models, based on coarse statistics, are simple and…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
Site-specific radio frequency (RF) propagation prediction increasingly relies on models built from visual data such as cameras and LIDAR sensors. When operating in dynamic settings, the environment may only be partially observed. This paper…
The rise of Generative AI (GenAI) in recent years has catalyzed transformative advances in wireless communications and networks. Among the members of the GenAI family, Diffusion Models (DMs) have risen to prominence as a powerful option,…
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers", as well as the scattering of coherent linear wave…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…