Champneys, AR

Cuevas, J

Kevrekidis, PG

Melvin, TRO

English

The present work examines in detail the existence, stability and dynamics of travelling solitary waves in dynamical lattices with saturable nonlinearity. After analszing the linear spectrum of the problem in the travelling wave frame, a pseudo-spectral numerical method is used to identify weakly non-local solitary waves. By finding zeros of an appropriately crafted tail condition, we can obtain the genuinely localised pulse-like solutions. Subsequent use of continuation methods allows us to obtain the relevant branches of solutions as a function of the system parameters, such as the frequency and inter-site coupling strength. We examine the stability of the solutions in two ways: both by imposing numerical perturbations and observing the solution dynamics, as well as by considering the solutions as fixed points of an appropriate map and computing the corresponding Floquet matrix and its eigenvalues. Both methods indicate that our solutions are robustly localised. Finally, the interactions of these solutions are examined in collision type phenomena, observing that relevant collisions are near-elastic, although they may, under appropriate conditions, lead to the generation of an additional pulse

Explore Bristol Research

A hybrid method for nonlinear algebraic equations”, Numerical Methods for Nonlinear Algebraic Equations.

A new barrier to the existence of moving kinks in Frenkel-Kontorova lattices”,

B.Sandstede & X.J.Wang. “Auto97 continuation and bifurcation software for ordinary differential equations”, ftp://ftp.es.concordia.ca/directory/doedel/auto

Bifurcation analysis of the localized modes dynamics in lattices with saturable nonlinearity”,

Bifurcations of travelling wave solutions in the discrete NLS equations”,

Breathers in nonlinear lattices: Existence, linear stability and quantization”,

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity”,

Discrete Solitons and Soliton-Induced Dislocations in Partially Coherent Photonic Lattices”,

Discrete solitons in photorefractive optically induced photonic lattices”,

Discretizing light behaviour in linear and nonlinear waveguide lattices”,

Do true elevation solitary waves exist? A numerical investigation”,

Dynamics of Bose-Einstein condensates in optical lattices”,

Growth and decay of discrete nonlinear Schrdinger breathers interacting with internal modes or standing-wave phonons”,

ıa, “Mobile localization in nonlinear Schrdinger lattices”,

ıc et al., “One-dimensional bright discrete solitons in media with saturable nonlinearity”,

Methods for discrete solitons in nonlinear lattices”,

Moving discrete breathers?”,

Moving lattice kinks and pulses: An inverse method”,

Moving solitons in the discrete nonlinear Schr¨ odinger equation”

Multi-pulse embedded solitons as bound states of quasi-solitons”,

Necklacelike Solitons in Optically Induced Photonic Lattices”,

Nonintegrable Schrdinger discrete breathers”,

Nonlinear dynamics and statistical physics of DNA”,

Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattice”,

Observation of discrete solitons in optically induced real time waveguidearrays”,

Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices”,

One-parameter localized traveling waves in nonlinear Schr¨ odinger lattices”,

Optical Solitons: From Fibers to Photonic Crystals”,

Power controlled soliton stability and steering in lattices with saturable nonlinearity”,

Quantum deformations of the discrete nonlinear Schrdinger equation“,

Radiationless Travelling Waves in

Sievers “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays”,

Solitons on lattices”,

Spatial photonics in nonlinear waveguide arrays”,

The Discrete Nonlinear Schr¨ odinger Equation: A Survey of Recent Results”,

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics”,

Travelling solitary waves in the discrete nonlinear Schrodinger equation with saturable nonlinearity: existence, stability and dynamics

https://research-information.bris.ac.uk/files/3006055/satDNLS_Final.pdf

Travelling solitary waves in the discrete nonlinear Schrodinger equation with saturable nonlinearity: existence, stability and dynamics

Abstract

Similar works

Full text

Available Versions

Explore Bristol Research