Related papers: Ideal Four Wave Mixing Dynamics in a Nonlinear Sch…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
The time evolution emanating from "internal dam-break" initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical…
Nonlinear wave mixing in mesoscopic silicon structures is a fundamental nonlinear process with broad impact and applications. Silicon nanowire waveguides, in particular, have large third-order Kerr nonlinearity, enabling salient and…
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.…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
Mediated by the interaction with quantum vacuum fields, a laser field propagating in a nonlinear optical medium can generate new light fields via spontaneous parametric process. Such process is inherent independent of the propagation…
In this paper, we present new results regarding the orbital stability of solitary standing waves for the general fourth-order Schr\"odinger equation with mixed dispersion. The existence of solitary waves can be determined both as minimizers…
We report on experimental and theoretical demonstration of an optical comb spectrum based on a combination of cascaded stimulated Raman scattering and four-wave mixing mediated by Raman-induced nonresonant Kerr-type nonlinearity. This…
The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
Quantum state coherent frequency conversion processes-such as Bragg scattering four wave mixing (BSFWM)-hold promise as a flexible technique for networking heterogeneous and distant quantum systems. In this letter, we demonstrate BSFWM…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To…
We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we…
Four-wave mixing and walk-off between two optical beams are investigated for fo cusing Kerr media. It is shown that four-wave mixing reinforces the self-focusi ng of mutually-trapped waves by lowering their power threshold for collapse, on…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
A correlated phase-and-additive-noise (CPAN) mismatched model is developed for wavelength division multiplexing over optical fiber channels governed by the nonlinear Schr\"odinger equation. Both the phase and additive noise processes of the…
Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…