Localised modes in discrete lattices

Lead Research Organisation: University of Bristol
Department Name: Engineering Mathematics and Technology

Abstract

Interplay between nonlinearity and periodicity is the focus of recent studies in different branches of modern applied mathematics and nonlinear physics. Our research program is in mathematical analysis of discrete dynamical systems. We aim to study nonlinear models expressed by the differential advanced-delay equations, difference equations and partial differential equations in the context of applications to photonic band-gap engineering, nonlinear optics, and atomic physics of Bose-Einstein condensates. The research program consists of several specific goals (problems): (1) derivation of the discrete nonlinear Schrodinger equation and the coupled-mode (Dirac) system, (2) persistence of traveling waves in discrete lattices, and (3) bifurcations and stability of three-dimensional discrete vortices.

Publications

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D Pelinovsky (2007) Discrete travelling solitons in the Salerno model in SIAM Journal of Applied Dynamical Systems

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Pelinovsky D (2007) One-parameter localized traveling waves in nonlinear Schrödinger lattices in Physica D: Nonlinear Phenomena

 
Description A new method for understanding exactly when true radiationless waves can travel through nonlinear lattices was developed. This led to further work with Panos Kevrekidis that has been widely influential in studying travelling localised modes in a wide variety of models.
Exploitation Route Used by Panos Kevrekidis one of the mostly widely cited scientists in nonlinear science. This has proved influential as a new methodology in nonlinear discrete wave equations.
Sectors Digital/Communication/Information Technologies (including Software)