Related papers: Modulation Instability and Phase-Shifted Fermi-Pas…
We give a qualitative explanation of the analog of the Fermi-Pasta-Ulam (FPU) recurrence in a one-dimensional focusing nonlinear Schrodinger equation (NLSE). That recurrence can be considered as a result of the nonlinear development of…
We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi--Pasta--Ulam (FPU) lattices. The growth of the instability is followed by a process of relaxation to…
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the…
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrodinger equation, the modulation instability (MI) of its n = 1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all…
The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive…
The integrable nonlinear Schr\"odinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a…
We consider the long-term weakly nonlinear evolution governed by the two-dimensional nonlinear Schr\"{o}dinger (NLS) equation with an isotropic harmonic oscillator potential. The dynamics in this regime is dominated by resonant interactions…
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear…
We show that, in the pure-quartic systems, modulation instability (MI) undergoes heteroclinic-structure transitions (HSTs) at two critical frequencies of {\omega} c1 and {\omega} c2 ( {\omega} c2 > {\omega} c1 ), which indicates that there…
We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which…
We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range…
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is…
The occurrence of the modulational instability (MI) in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity…
The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam - $\beta$ system is numerically investigated. No external perturbation is considered for the one-mode exact analytical solutions, the only perturbation being that…
In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable…
We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a…
The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is…
The instabilities of the nontrivial phase elliptic solutions in a repulsive Bose-Einstein condensate (BEC) with a periodic potential are investigated. Based on the defocusing nonlinear Schr\"{o}dinger (NLS) equation with an elliptic…
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…
We investigate the modulation instability of multiple four-wave mixing arising from a dual-frequency pump in a single-mode fiber or waveguide. By applying the Floquet theory on account of the periodic nature of four-wave mixing, we reveal a…