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Using a variational approximation we study discrete solitons of a nonlinear Schroedinger lattice with a cubic-quintic nonlinearity. Using an ansatz with six parameters we are able to approximate bifurcations of asymmetric solutions…

Pattern Formation and Solitons · Physics 2009-04-23 C. Chong , D. E. Pelinovsky

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling…

Pattern Formation and Solitons · Physics 2015-05-20 F. Kh. Abdullaev , P. G. Kevrekidis , M. Salerno

We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the…

Pattern Formation and Solitons · Physics 2009-11-11 J. Gomez-Gardenes , L. M. Floria , A. R. Bishop

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…

Pattern Formation and Solitons · Physics 2022-01-05 Faustino Palmero , Mario I. Molina , Jesús Cuevas-Maraver , Panayotis G. Kevrekidis

The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised…

Pattern Formation and Solitons · Physics 2022-05-04 Dirk Hennig , Nikos I. Karachalios , Jesus Cuevas-Maraver

We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…

Pattern Formation and Solitons · Physics 2007-05-23 R. H. Goodman , P. J. Holmes , M. I. Weinstein

In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation near anti-continuous limit. Our novel insight is that the analysis of linearized operator, usually…

Analysis of PDEs · Mathematics 2021-12-03 Masaya Maeda , Masafumi Yoneda

In the present Letter we use the Wannier function basis to construct lattice approximations of the nonlinear Schr\"{o}dinger equation with a periodic potential. We show that the nonlinear Schr\"{o}dinger equation with a periodic potential…

Condensed Matter · Physics 2009-11-07 G. L. Alfimov , P. G. Kevrekidis , V. V. Konotop , M. Salerno

We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete…

Pattern Formation and Solitons · Physics 2009-11-11 Andrea Fratalocchi , Gaetano Assanto

We explore driven lattice gases for the existence of an intensive thermodynamic variable which could determine "equilibration" between two nonequilibrium steady-state systems kept in weak contact. In simulations, we find that these systems…

Statistical Mechanics · Physics 2015-05-07 Punyabrata Pradhan , Christian P. Amann , Udo Seifert

The dynamics in a nonlinear Schrodinger chain in an homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster…

Pattern Formation and Solitons · Physics 2007-05-23 F. J. Cao

The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of…

General Physics · Physics 2012-09-28 Jean-Jacques Sinou , Fabrice Thouverez

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…

Optics · Physics 2011-07-05 Guenbo Hwang , T. R. Akylas , Jianke Yang

Analysis of the nonlinear Schrodinger vortex reconnection is given in terms of coordinate-time power series. The lowest order terms in these series correspond to a solution of the linear Schrodinger equation and provide several interesting…

Fluid Dynamics · Physics 2009-09-29 S. Nazarenko , R. J. West

In the present work we study discrete nonlinear Schr{\"o}dinger models combining nearest (NN) and next-nearest (NNN) neighbor interactions, motivated by experiments in waveguide arrays. While we consider the more experimentally accessible…

Pattern Formation and Solitons · Physics 2025-06-30 Christopher J. Lustri , Inês Aniceto , Panayotis G. Kevrekidis

The problem of showing the existence of localised modes in nonlinear lattices has attracted considerable efforts from the physical but also from the mathematical viewpoint where a rich variety of methods has been employed. In this paper we…

Analysis of PDEs · Mathematics 2021-12-08 Dirk Hennig , Nikos I. Karachalios

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…

Pattern Formation and Solitons · Physics 2013-11-28 R. K. Jackson , R. Marangell , H. Susanto

We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the…

Pattern Formation and Solitons · Physics 2015-06-23 P. G. Kevrekidis , B. A. Malomed , A. Saxena , D. J. Frantzeskakis , A. R. Bishop

We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant…

Quantum Gases · Physics 2021-02-24 Lorenzo Gotta , Leonardo Mazza , Pascal Simon , Guillaume Roux

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy…

Pattern Formation and Solitons · Physics 2008-12-18 Michael Oster , Magnus Johansson