Related papers: Modulational instability of Geodesic-Acoustic-Mode…
We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We consider wavepackets composed of two modulated carrier Bloch waves with opposite group velocities in the one dimensional periodic Nonlinear Schroedinger/Gross-Pitaevskii equation. These can be approximated by first order coupled mode…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
Modulational instability (MI) of dust acoustic waves (DAWs), which propagates in an opposite polarity dusty plasma system, containing inertial warm negatively and positively charged dust particles as well as non-extensive q-distributed…
We study the linear dynamics of spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. Such $T$-periodic solutions…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We examine the modulational instability (MI) of ion-acoustic waves (IAWs) in an electronegative plasma containing positive and negative ions as well as electrons that follow the nonextensive statistics proposed by Tsallis [J. Stat. Phys.…
We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have…
We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity…
The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schroedinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
Nonlinear stage of higher-order modulation instability (MI) phenomena in the frame of multicomponent nonlinear Schr\"odinger equations (NLSEs) are studied analytically and numerically. Our analysis shows that the $N$-component NLSEs can…
A four component space plasma system (consisting of immobile positive ions, inertial cold positrons as well as hot electrons and positrons following Cairns' nonthermal distribution function is considered. The nonlinear propagation of the…
We investigate the growth of ion density perturbations in large-amplitude linear laser wakefields via two-dimensional particle-in-cell simulations. Growth rates and wave numbers are found to be consistent with a longitudinal strong-field…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
We review recent results on the nonlinear development of thermal instability in the context of the turbulent atomic interstellar medium (ISM). First, we pre- sent a brief summary of the linear theory, remarking that, in the atomic ISM, the…
An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation…
Motivated by the central phenomenon of energy cascades in wave turbulence theory, we construct non-equilibrium statistical steady states (NESS), or invariant measures, for a simplified model derived from the nonlinear Schr\"odinger (NLS)…