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Related papers: Gap and out-gap breathers in a binary modulated di…

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Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and…

Pattern Formation and Solitons · Physics 2020-05-13 Gennady El , Alexander Tovbis

Discrete nonlinear Schrodinger equation (DNLS) describes a chain of oscillators with nearest neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to…

Mathematical Physics · Physics 2007-05-23 Nickolay Korabel , George M. Zaslavsky

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown…

We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…

Exactly Solvable and Integrable Systems · Physics 2019-10-15 Bao-Feng Feng , Liming Ling , Daisuke A. Takahashi

Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by…

Pattern Formation and Solitons · Physics 2007-05-23 Magnus Johansson

We investigate the spectral stability of non-degenerate vector soliton solutions and the nonlinear stability of breather solutions for the coupled nonlinear Schrodinger (CNLS) equations. The non-degenerate vector solitons are spectrally…

Exactly Solvable and Integrable Systems · Physics 2024-11-14 Liming Ling , Dmitry E. Pelinovsky , Huajie Su

We study a variable-coefficient nonlinear Schr\"odinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak…

Pattern Formation and Solitons · Physics 2016-06-22 Lei Wang , Jian-Hui Zhang , Chong Liu , Min Li , Feng-Hua Qi

We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schr\"odinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a…

Chaotic Dynamics · Physics 2021-05-12 Stefano Iubini , Antonio Politi

We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…

Analysis of PDEs · Mathematics 2008-05-27 E. Kirr , A. Zarnescu

IN-DNLS, considered here is a countable infinite set of coupled one dimensional nonlinear ordinary differential difference equations with a tunable nonlinearity parameter, $\nu$. This equation is continuous in time and discrete in space…

Pattern Formation and Solitons · Physics 2007-05-23 K. Kundu

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of…

Pattern Formation and Solitons · Physics 2007-05-23 F. R. Romero , J. F. R. Archilla , F. Palmero , B. Sanchez-Rey , A. Alvarez , J. Cuevas , J. M. Romero

We consider the periodic standing waves in the derivative nonlinear Schrodinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all periodic standing waves in terms of…

Exactly Solvable and Integrable Systems · Physics 2021-05-19 Jinbing Chen , Dmitry E. Pelinovsky , Jeremy Upsal

In the present investigation, the solutions on the periodic and double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the…

Exactly Solvable and Integrable Systems · Physics 2021-11-30 H. J. Zhou , Y. Chen

In the present work, we explore the possibility of excited breather states in a nonlinear Klein--Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this fundamentally nonlinear…

Pattern Formation and Solitons · Physics 2015-05-13 Jesús Cuevas-Maraver , Panayotis G. Kevrekidis , Dmitry E. Pelinovsky

The paper addresses compact oscillatory states (compact breathers) in translationally-invariant lattices with flat dispersion bands. The compact breathers appear in such systems even in the linear approximation. If the interactions are…

Pattern Formation and Solitons · Physics 2020-08-31 Nathan Perchikov , O. V. Gendelman

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend…

Pattern Formation and Solitons · Physics 2015-05-20 J. Cuevas , P. G. Kevrekidis , A. Saxena , A. Khare

We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed…

patt-sol · Physics 2009-10-31 A. E. Kozhekin , G. Kurizki , Boris A. Malomed

We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the…

Pattern Formation and Solitons · Physics 2009-11-07 P. G. Kevrekidis , B. A. Malomed , Yu. B. Gaididei

We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By…

Exactly Solvable and Integrable Systems · Physics 2018-03-20 Annalisa Calini , Constance M. Schober

Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and delocalization phenomena. $q$-Breathers -- periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear…

Pattern Formation and Solitons · Physics 2009-11-13 M. V. Ivanchenko