Related papers: Modulational instability in periodic quadratic non…
We study the higher order harmonics of scalar modulational instability in the regime where it arises spontaneously through amplification of vacuum fluctuations. We obtain detailed predictions concerning the detunings, intensities, growth…
We study the modulational instability of periodic traveling waves for a class of Hamiltonian systems in one spatial dimension. We examine how the Jordan block structure of the associated linearized operator bifurcates for small values of…
Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…
In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift…
We present an analysis of temporal modulation instability in a ring array of coupled optical fibers. Continuous-wave signals are shown to be unstable to perturbations carrying discrete angular momenta, both for normal and anomalous group…
Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred to as flexural-gravity waves. We compare and contrast two…
A novel grating modulation technique for laser arrays is proposed and demonstrated. This method modifies the initial phase within each grating period, applying a total phase shift that increments in an arithmetic progression, ensuring equal…
Nonlinear dynamics emerge through either nonlinear interactions between the variables or through nonlinearities imposed on their linear interactions. Their interactions can be conceptualized as modulations of input-output (I/O) functions,…
We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented…
We study the Floquet edge states in arrays of periodically curved optical waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the bulk-edge correspondence, our study explores the interplay between band topology and…
We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the…
We show that a grating amplitude stationary in space but oscillating in time can be accurately modelled as a set of independent gratings travelling in opposite directions, interacting almost exclusively with waves travelling in the same…
We propose a multi-field-coupled atomic model that exhibits controllable $symmetric$ and $asymmetric$ evolution of significantly enhanced diffraction peaks in an opto-atomic grating at far-field regime. Such results are obtained by the…
We present a solver for plane wave scattering from a periodic dielectric grating with a large number $M$ of inclusions lying in each period of its middle layer.Such composite material geometries have a growing role in modern photonic…
This study introduces the Bragg Frequency Convertor, a spatial-temporal-periodic grating that extends the concept of conventional Bragg gratings into the dynamic domain to achieve pure parametric frequency conversion. By time-modulating…
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…
This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability…
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of…
The occurrence of non-adiabatic effects in the vibrational properties of metals have been predicted since the 60's, but hardly confirmed experimentally. We report the first fully \emph{ab initio} calculations of non-adiabatic frequencies of…