Related papers: Bound state soliton gas dynamics underlying the no…
A theoretical investigation has been made to study the modulation stability/instability of three-dimensional dust-ion-acoustic wave packets in the warm magnetized complex plasma system in the presence of nonthermal distributed electrons and…
The modulational instability (MI) criteria of dust-ion-acoustic (DIA) waves (DIAWs) have been investigated in a four-component pair-ion plasma having inertial pair-ions, inertialess non-thermal non-extensive electrons, and immobile…
The existence of stable bound states of three solitons in a Bose-Einstein condensate with nonlocal interactions is demonstrated by means of variational approach (VA) and numerical simulations. The potential of interaction between solitons…
We review the modulation stability of parallel propagating/field aligned Whistler Mode Chorus waves propagating in a warm plasma from a formal perspective with a focus on wave-particle interactions. The modulation instability criteria is…
We study experimentally the Bloch-wave instabilities in optically-induced lattices. We reveal two different instability scenarios associated with either the transverse modulational instability of a single Bloch wave, or the nonlinear…
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…
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…
Binary discrete nonlinear Schr\"odinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime…
Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By…
We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit…
The influence of a saturable nonlinearity on the modulation instability in oppositely directed coupler in the presence of high-order effects is investigated. By using the standard linear stability analysis, we obtain the instability gain…
An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic…
We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field…
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…
In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane…
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are…
It has been established for some time that high-power pump can trap a probe beam of lower intensity that is simultaneously propagating in a Kerr-type optical medium, inducing a focusing of the probe with the emergence of modes displaying…
We consider dynamical stabilization of Bose-Einstein condensates (BEC) by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments,…
Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing.…
We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger…