Related papers: Extreme events in discrete nonlinear lattices
The Ablowitz-Ladik equations, hereafter called $AL_+$ and $AL_-$, are distinguished integrable discretizations of respectively the focusing and defocusing nonlinear Schr\"odinger (NLS) equations. In this paper we first study the modulation…
We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate creation of traveling solitons in the lattice. We predict this possibility in an…
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. So far, nonlinear stability of such…
We study the statistical mechanics of the one-dimensional discrete nonlinear Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
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…
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators…
We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they…
We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
We investigate the outbreak of anomalous quantum wavefunction amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and…
A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave…
The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling…
Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust particles as…
In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relevant lattice nonlinear dynamical systems. Starting from the…
We study numerically the integrable turbulence developing from strongly nonlinear partially coherent waves, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. We find that shortly after the beginning of motion…
Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term…
We study the bulk and surface nonlinear modes of the modified one-dimensional discrete nonlinear Schroedinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the…
We study on the relations between modulational instability and several well-known nonlinear excitations in a nonlinear fiber, such as bright soliton, nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and Kuznetsov-Ma…