English
Related papers

Related papers: Discrete solitons in electromechanical resonators

200 papers

We study a discrete nonlinear Schr\"odinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and…

We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons…

Mathematical Physics · Physics 2009-08-18 Eamonn Long , David Stuart

We study a quasilinear Schr\"odinger equation with nonzero conditions at infinity. In previous works, we obtained a continuous branch of traveling waves, given by dark solitons indexed by their speed. Neglecting the quasilinear term, one…

Analysis of PDEs · Mathematics 2026-05-18 Erwan Le Quiniou

In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…

Analysis of PDEs · Mathematics 2007-12-10 J. Bellazzini , V. Benci , C. Bonanno , A. M. Micheletti

We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…

Analysis of PDEs · Mathematics 2025-04-25 Rik W. S. Westdorp , Hermen Jan Hupkes

In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical…

Quantum Gases · Physics 2019-12-04 Wenlong Wang , P. G. Kevrekidis , Egor Babaev

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the…

Dynamical Systems · Mathematics 2016-09-21 D. Pelinovsky , T. Penati , S. Paleari

Black solitons are identical in the nonlinear Schr\"{o}dinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties in the…

Analysis of PDEs · Mathematics 2022-05-23 Dmitry E. Pelinovsky , Michael Plum

The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently in [de Laire and S. L\'opez-Mart\'inez,…

Numerical Analysis · Mathematics 2023-05-03 André de Laire , Guillaume Dujardin , Salvador López-Martínez

We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…

Pattern Formation and Solitons · Physics 2015-06-04 Olga V. Borovkova , Valery E. Lobanov , Boris A. Malomed

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…

Pattern Formation and Solitons · Physics 2012-05-11 C. Chong , R. Carretero-Gonzalez , B. A. Malomed , P. G. Kevrekidis

We study the influences to the discrete soliton (DS) by introducing linearly long-range nonlocal interactions, which give rise to the off-diagonal elements of the linearly coupled matrix in the discrete nonlinear schrodinger equation to be…

Optics · Physics 2014-11-24 Zhijie Mai , Shenhe Fu , Jianxiong Wu , Yongyao Li

Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons…

Pattern Formation and Solitons · Physics 2009-11-13 A. S. Rodrigues , P. G. Kevrekidis , Mason A. Porter , D. J. Frantzeskakis , P. Schmelcher , A. R. Bishop

We reveal the existence of slowly-decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schr\"odinger…

Pattern Formation and Solitons · Physics 2016-04-06 R. I. Woodward , E. J. R. Kelleher

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schr\"odinger equation. When the nonlinearity is of the cubic type, this amplitude is…

Pattern Formation and Solitons · Physics 2013-05-29 O. F. Oxtoby , I. V. Barashenkov

We study collisions of moving nonlinear-Schr\"{o}dinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and,…

Pattern Formation and Solitons · Physics 2016-11-03 N. Karjanto , W. Hanif , B. A. Malomed , H. Susanto

The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices,…

Other Condensed Matter · Physics 2009-11-10 L. D. Carr , Charles W. Clark

We study the 1D dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate ($g>0$). By using an adiabatic perturbation theory in…

Quantum Gases · Physics 2018-04-25 I. Morera , A. Muñoz Mateo , A. Polls , B. Juliá-Díaz

Discrete bright breathers are well known phenomena. They are localized excitations that consist of a few excited oscillators in a lattice and the rest of them having very small amplitude or none. In this paper we are interested in the…

Pattern Formation and Solitons · Physics 2009-11-07 A. Alvarez , J. F. R. Archilla , J. Cuevas , F. R. Romero

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