Related papers: Statistics of wave interactions in nonlinear disor…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…
Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with…
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…
This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…
Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…
Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
We consider the problem of sliding motion of a charge-density-wave subject to static disorder within an elastic medium model. Starting with a field-theoretical formulation, which allows exact disorder averaging, we propose a self-consistent…
A robust energy transfer mechanism is found in nonlinear wave systems, which favours transfers towards modes interacting via non-resonant triads, applicable in meteorology, nonlinear optics and plasma wave turbulence. Transfer efficiency is…
The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless…