Details of Grant 

EPSRC Reference:	EP/D065623/1
Title:	Localised modes in discrete lattices
Principal Investigator:	Champneys, Professor AR
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Engineering Mathematics and Technology
Organisation:	University of Bristol
Scheme:	Standard Research
Starts:	04 December 2006	Ends:	03 September 2007	Value (£):	22,925
EPSRC Research Topic Classifications:	Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:	EP/D069513/1
Panel History:
Summary on Grant Application Form
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.
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Organisation Website:	http://www.bris.ac.uk