We investigate the modulational instability of nonlinear Schrödinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach Resonance Management for Bose-Einstein condensates. We derive the corresponding linear stability equation analytically and we show that it can be reduced to a Kro...

The generalized Charney-Hasegawa-Mima equation is unstable to a four wave modulational instability whereby a coherent, monochromatic drift wave can drive a band of modes and associated zonal flows unstable. Although initially the fastest growing modes dominate, a secondary nonlinear instability later drives the longest wavelength zonal flow and its associated sidebands at twice the growth rate ...

This Letter reports the first experimental demonstration of chaotic excitations through modulational instability for waves with a repulsive nonlinearity. The experiments were carried out for surface spin waves in a magnetic thin film strip in an active feedback ring configuration. At a low ring gain level, one observes the self-generation of one eigenmode. With an increase in the ring gain, one...

Creation of better statistical models for improvement of existing operational wave prediction programs; study of non-stationary waves growth in presence of wind; interpretation of experimental data through study of self-similar solutions of Hasselmann equation; studying the integrability of 1D dynamical equations for surface waves; study of the possibility of generalization of compact 1D water ...

In continuously stratified fluid, vertically propagating internal gravity waves of moderately large amplitude can become unstable and possibly break due to a variety of mechanisms including with some overlap modulational instability, parametric subharmonic instability PSI , self-acceleration, overturning, and convective instability. In PSI, energy from primary waves is transferred, for example,...

We report the observation of modulational instability (MI) of a partially spatially incoherent beam induced by seeding noise through cross-phase modulation. We show experimentally that a threshold exists for such induced incoherent MI to occur that depends on the degree of spatial coherence as well as on the strength of the nonlinearity. Above threshold, the induced MI leads to the formation of...

Excitation of unbalanced-Bessel beams by a gradual increase of nonlinearity in a water sample outlines the achievement of the first ever observed quasimonochromatic wave packet that propagates stably for hundreds of Rayleigh lengths in a focusing and dispersive Kerr medium, i.e., in the absence of spectral broadening and conical emission. A modulational instability analysis reveals the key role...

We present a statistical description of the propagation of short pulses in long optical fibers, taking into account the Kerr and nonlocal nonlinearities on an equal footing. We use the Wigner approach on the modified nonlinear Schrödinger equation to obtain a wave kinetic equation and a nonlinear dispersion relation. The latter shows that the optical pulse decoherence reduces the growth rate of...

Continuous plasma coherent emission is maintained by repetitive Langmuir collapse driven by the nonlinear evolution of a strong electron two-stream instability. The Langmuir waves are modulated by solitary waves in the linear stage and electrostatic whistler waves in the nonlinear stage. Modulational instability leads to Langmuir collapse and electron heating that fills in cavitons. The high pr...

The modulational instability (MI) of ion-acoustic waves (IAWs) is examined theoretically in a four-component plasma system containing inertialess electrons featuring non-thermal, non-extensive distribution, iso-thermal positrons, and positively as well negatively charged inertial ions. In this connection, non-linear Schrödinger equation (NLSE), which dominates the conditions for MI associated w...