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We investigate the dynamics of modulational instability (MI) in $\cal PT$-symmetric fiber Bragg gratings with a phenomenon of intermodulation known as four-wave mixing (FWM). Although the impact of FWM has already been analyzed in the…

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…

Pattern Formation and Solitons · Physics 2015-06-03 P. G. Kevrekidis , D. E. Pelinovsky , A. Saxena

The one-dimensional focusing nonlinear Schrodinger equation (NLSE) on an unstable condensate background is the fundamental physical model, that can be applied to study the development of modulation instability (MI) and formation of rogue…

Exactly Solvable and Integrable Systems · Physics 2018-02-14 A. A. Gelash

In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete…

Applied Physics · Physics 2023-05-31 Antoine Demiquel , Vassos Achilleos , Georgios Theocharis , Vincent Tournat

In this work, we investigate the modulational instability of plane wave solutions within a modified Gross-Pitaevskii equation framework. The equation features cubic and quartic nonlinearity. It models the behaviour of quasi-one-dimensional…

Quantum Gases · Physics 2024-05-20 Sherzod R. Otajonov , Bakhram A. Umarov , Fatkhulla Kh. Abdullaev

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…

Pattern Formation and Solitons · Physics 2012-06-07 F. Maucher , W. Krolikowski , S. Skupin

Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schr\"odinger equation (NLSE) [E. Poli, Phys. Plasmas 2021]. This equation predicts susceptibility of GAM packets to the…

We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…

Pattern Formation and Solitons · Physics 2014-10-15 Taras I. Lakoba

The long-time asymptotic behavior of the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric nonzero boundary conditions at infinity is characterized by using the recently developed inverse scattering transform (IST)…

Analysis of PDEs · Mathematics 2015-12-21 Gino Biondini , Dionyssios Mantzavinos

The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in…

Soft Condensed Matter · Physics 2015-06-24 Z. Rapti , P. G. Kevrekidis , D. J. Frantzeskakis , B. A. Malomed

The spatially periodic breather solutions (SPBs) of the nonlinear Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the effects of nonlinear dissipation and higher order…

Pattern Formation and Solitons · Physics 2022-06-15 C. M. Schober , A. Islas

We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic…

Pattern Formation and Solitons · Physics 2023-06-14 Gennady A. El

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…

Pattern Formation and Solitons · Physics 2009-11-11 I. Kourakis , P. K. Shukla

By means of linear stability analysis (LSA) and direct numerical simulations of the coupled Gross-Pitaevskii(GP)equations, we address the impurity induced modulational instability (MI) and the associated nonlinear dynamics in Bose-Einstein…

Quantum Gases · Physics 2023-01-30 Ishfaq Ahmad Bhat , Bishwajyoti Dey

The dynamics of soliton pulses in the Nonlinear Schrodinger Equation (NLSE) driven by an external Traveling wave is studied analytically and numerically. The Hamiltonian structure of the system is used to show that, in the adiabatic…

patt-sol · Physics 2009-10-31 Gil Cohen

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The…

Soft Condensed Matter · Physics 2009-11-10 L. D. Carr , J. Brand

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in…

Pattern Formation and Solitons · Physics 2021-08-31 Josselin Garnier , Kilian Baudin , Adrien Fusaro , Antonio Picozzi

We quantify noise-induced phase deviations of dispersion-managed solitons in optical fiber communications and femtosecond lasers. We first develop a perturbation theory for the dispersion-managed nonlinear Schrodinger equation (DMNLSE) in…

Pattern Formation and Solitons · Physics 2009-07-15 Elaine Spiller , Gino Biondini

Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…

Pattern Formation and Solitons · Physics 2015-08-25 S. Kumar , R. Herrero , M. Botey , K. Staliunas

The modulational instability and discrete matter wave solitons in dipolar BEC, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a…

Quantum Gases · Physics 2015-05-28 S. Rojas-Rojas , R. A. Vicencio , M. I. Molina , F. Kh. Abdullaev