Related papers: Modulational instability in randomly dispersion-ma…
We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schr\"{o}dinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
We present detailed experimental study on noise-seeded intermodal modulation instability (IM-MI) in normal dispersion region of a conventional step-index fiber. The sharp refractive index contrast between core and cladding leads to large…
We have investigated modulation instability in metamaterials (MM) with both cubic and quintic nonlinearities, based on a model appropriate for pulse propagation in MMs with cubic-quintic nonlinearities and higher order dispersive effects.…
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…
We report an optical fiber experiment in which we study nonlinear stage of modulational instability of a plane wave in the presence of a localized perturbation. Using a recirculating fiber loop as experimental platform, we show that the…
In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic-quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by…
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model based on the non-linear Schrodinger equation…
The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete…
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order…
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 study the linear evolution of small perturbations in self-gravitating fluid systems with magnetic fields. We consider wave-like perturbations to nonuniform filamentary and sheet-like hydrostatic equilibria in the presence of a uniform…
Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…