Related papers: Hydrodynamic modulation instability triggered by a…
On examples of Bose-Einstein condensates embedded in two-dimensional optical lattices we show that in nonlinear periodic systems modulational instability and inter-band tunneling are intrinsically related phenomena. By direct numerical…
The nonlinear Schr{\"o}dinger (NLS) equation is a ubiquitous example of an envelope wave equation for conservative, dispersive systems. We revisit here the problem of self-similar focusing of waves in the case of the focusing NLS equation…
We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial…
The focusing NLS equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, considered the main physical mechanism for the appearance of rogue (anomalous)…
Theoretical and numerical studies are presented of the nonlinear amplitude modulation of dust-acoustic (DA) waves propagating in an unmagnetized three component, weakly-coupled, fully ionized plasma consisting of electrons, positive ions…
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…
The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background…
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The…
The dynamics and stability of continuous-wave and multi-pulse structures are studied theoretically, for a generalized model of passively mode-locked fiber laser with an arbitrary nonlinearity. The model is characterized by a complex…
We study numerically the integrable turbulence in the framework of the focusing one-dimensional nonlinear Schrodinger equation using a new method -- the "growing of turbulence". We add to the equation a weak controlled pumping term and…
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 work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require…
Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane…
The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated…
It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrodinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic…
The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…
We investigate the influence of rotation on the onset and saturation of the Faraday instability in a vertically oscillating two-layer miscible fluid using a theoretical model and direct numerical simulations (DNS). Our analytical approach…
We propose a simple phenomenological model for describing the conformational dynamics of biopolymers via the nonlinearity-induced buckling and collapse (i.e. coiling up) instabilities. Taking into account the coupling between the internal…
This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the strong instability of standing waves associated with ground state solutions in the $L^2$-supercritical case.…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…