We study the modulational instability in surface gravity waves with random phase spectra. Starting from the nonlinear Schrödinger equation and using the Wigner-Moyal transform, we study the stability of the narrow-banded approximation of a typical wind-wave spectrum, i.e., the JONSWAP spectrum. By performing numerical simulations of the nonlinear Schrödinger equation we show that in the unstabl...

We study rational solutions of continuous wave backgrounds with the critical frequencies of the Sasa-Satsuma equation, which can be used to describe the evolution of the optical field in a nonlinear fiber with some high-order effects. We find a striking dynamical process that two W-shaped solitons are generated from a weak modulation signal on the continuous wave backgrounds. This provides a po...

The modulational instability, a destabilization mechanism for plane waves, occurs ubiquitously in spatially extended dynamical systems arising in fluid dynamics, nonlinear optics, atomic physics, and other disciplines. In this paper, we investigate analytically, numerically, and experimentally the modulational instability in a layered cubically nonlinear (Kerr) optical medium that consists of a...

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma. Keywords—Amplitude Modulation, Electron Pla...

The modulation instability of the one-dimensional cubic-quintic complex Ginzburg-Landau equation with fouth-order dispersion and gain terms, a. k. a., the quintic complex Swift-Hohenberg equation, is investgated. The effects of the fourth-order terms to the modulational instability is studied. We numerically investigate the dynamics of the modulational instability in the presence of the fourtho...

Antiferromagnetic condensates are generally believed not to display modulational instability and subsequent spin-domain formation. Here we demonstrate that in the presence of a homogeneous magnetic field antiferromagnetic spin-1 Bose-Einstein condensates can undergo spatial modulational instability followed by the subsequent generation of spin domains. Employing numerical simulations for realis...

We consider the temporal evolution of an incoherent optical wave that propagates in a noninstantaneous response nonlinear medium, such as single mode optical fibers. In contrast with the expected Raman-like spectral redshift due to a delayed nonlinear response, we show that a highly noninstantaneous response leads to a genuine modulational instability of the incoherent optical wave. We derive a...

We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of alternating glass-air layers, is the piecewise-constant nature of the material properties, which allows a theoretical linear stability analysis leading to a Kronig-Penney equation whose forbidden bands corres...

  Propagation of dust ion acoustic waves in plasmas composed of nonthermal distributed electrons and stationary dust particles is investigated. Nonlinear Schrdinger equation is derived to describe small amplitude waves, using the reduction perturbation technique. Modulation instability of dust ion acoustic waves is analysed for this system. Parametric investigation indicates that growth rate of...

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...