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We consider the Sasa-Satsuma (SS) and Nonlinear Schr\"odinger (NLS) equations posed along the line, in 1+1 dimensions. Both equations are canonical integrable $U(1)$ models, with solitons, multi-solitons and breather solutions, see Yang for…

Analysis of PDEs · Mathematics 2021-02-24 Miguel A. Alejo , Luca Fanelli , Claudio Muñoz

Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schroedinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave…

solv-int · Physics 2007-05-23 S. Lee , Julian J. -L. Ting , S. Kim

This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schr\"odinger equation (N LS) with non-zero condition at infinity. The aim of this article is twofold.…

Analysis of PDEs · Mathematics 2026-04-01 Jordan Berthoumieu

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor,…

Pattern Formation and Solitons · Physics 2015-05-22 F. Palmero , L. Q. English , J. Cuevas , R. Carretero-González , P. G. Kevrekidis

In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…

Analysis of PDEs · Mathematics 2026-04-13 Jaime Angulo Pava , Alexander Muñoz

In the present work, we develop a systematic examination of the existence, stability and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an…

Pattern Formation and Solitons · Physics 2010-12-14 C. Hoogeboom , G. Theocharis , P. G. Kevrekidis

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit…

Pattern Formation and Solitons · Physics 2024-03-08 Peng Gao , Li-Zheng Lv , Xin Li

We study metastable behavior in a discrete nonlinear Schr\"odinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy…

Dynamical Systems · Mathematics 2020-10-28 Jean-Pierre Eckmann , C. Eugene Wayne

Recently, a novel bifurcation technique known as the deflated continuation method (DCM) was applied to the single-component nonlinear Schr\"odinger (NLS) equation with a parabolic trap in two spatial dimensions. The bifurcation analysis…

Pattern Formation and Solitons · Physics 2020-06-24 E. G Charalampidis , N. Boullé , P. E. Farrell , P. G. Kevrekidis

We demonstrate that period-doubled discrete breathers appear from the anti-continuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between sub-harmonic solutions of the driven…

Pattern Formation and Solitons · Physics 2011-01-13 P. Maniadis , B. S. Alexandrov , A. R. Bishop , K. Ø. Rasmussen

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…

Condensed Matter · Physics 2009-10-31 J. C. Bronski , L. D. Carr , B. Deconinck , J. N. Kutz , K. Promislow

The basic features of nucleus-acoustic (NA) envelope bright and dark solitons, which exist in degenerate quantum plasmas, have been theoretically investigated by deriving the nonlinear Schr\"odinger (NLS) equation. The reductive…

Plasma Physics · Physics 2017-06-20 N. A. Chowdhury , M. M. Hasan , A. Mannan , A. A. Mamun

We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schr\"{o}dinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of {\em…

Pattern Formation and Solitons · Physics 2007-05-23 D. E. Pelinovsky , P. G. Kevrekidis , D. J. Frantzeskakis

The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…

Pattern Formation and Solitons · Physics 2024-08-22 P. G. Kevrekidis , D. E. Pelinovsky , R. M. Ross

Nonlinear stage of higher-order modulation instability (MI) phenomena in the frame of multicomponent nonlinear Schr\"odinger equations (NLSEs) are studied analytically and numerically. Our analysis shows that the $N$-component NLSEs can…

Pattern Formation and Solitons · Physics 2025-04-15 Shao-Chun Chen , Chong Liu

We study the stability properties of periodic solutions to the Nonlinear Schr\"odinger (NLS) equation with a periodic potential. We exploit the symmetries of the problem, in particular the Hamiltonian structure and the $\U(1)$ symmetry. We…

Pattern Formation and Solitons · Physics 2007-05-23 Jared C. Bronski , Zoi Rapti

We derive a nonlinear Schroedinger equation with a radical term, in the form of the square root of (1-|V|^2), as an asymptotic model of the optical medium built as a periodic set of thin layers of two-level atoms, resonantly interacting…

Optics · Physics 2015-05-27 Lior Shabtay , Boris A. Malomed

We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…

Pattern Formation and Solitons · Physics 2017-05-18 Itay Grinberg , Oleg V. Gendelman

We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between…

Pattern Formation and Solitons · Physics 2013-10-25 Dirk Hennig

We study a fractional version of the two-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation, where the usual discrete Laplacian is replaced by its fractional form that depends on a fractional exponent $s$ that interpolates…

Pattern Formation and Solitons · Physics 2020-07-08 Mario I. Molina