Localised modes in discrete lattices
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
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.
Organisations
People |
ORCID iD |
Robert MacKay (Principal Investigator) |
Publications
Pelinovsky D
(2008)
Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential
in Communications in Mathematical Physics
Description | We attempted to prove existence of breathers in lattices in a context close to continuum. We managed this but only under restricted hypotheses. |
Exploitation Route | It might be possible to extend to our original goal. |
Sectors | Other |
Description | Our paper has 16 citations according to Google Scholar |
First Year Of Impact | 2008 |
Sector | Other |