Details of Grant 

EPSRC Reference:	GR/J22993/01
Title:	NON-LINEAR LATTICE SYSTEMS AND DATA TRANSMISSION
Principal Investigator:	Common, Dr A
Other Investigators:	Sobhy, Professor M
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Kent
Scheme:	Standard Research (Pre-FEC)
Starts:	10 February 1994	Ends:	09 February 1996	Value (£):	55,966
EPSRC Research Topic Classifications:	Networks & Distributed Systems
EPSRC Industrial Sector Classifications:
Related Grants:
Panel History:
Summary on Grant Application Form
1) To investigate the derivation of soliton and shock solutions supported by nonlinear lattice systems with particular emphasis placed upon lattices equivalent to nonlinear transmission lines.2) To study propagation properties of nonlinear transmissions lines as pulse shortening circuits.3) To study the propagation properties of multi- mode transmissions media and inter-symbol interference.4) To design nonlinear filters.Progress:The project began with a review of the available literature on the subject of Nonlinear Transmissions Lines (NLTLs). A study of NLTLs was then undertaken from both a practical and theoretical viewpoint.The practical part of the investigation involved the verification of results presented by a Californian group (see e.g. Case et al. Appl. Phys. Lett 61 (1992)) that had fabricated the simulated NLTLs on Gallium Arsenide substrates and whose devices supported solitary wave pulse propagation with the pulse half-widths in the picosecond regime. We were able to verify their results when the NLTL was homogeneous using the HSPICE circuit analysis package, promoting confidence in the use of the package. We investigated the effect of different diode models and the input of pulses of differing widths and spaces onto the line. We found that the ideal NLTL supported solitary waves. In particular we investigated applying more than one pulse onto the line (inter-symbol inference) and found the pulses behaved like solitons. As pulse shortening circuits we found the NTLSs performed better when the diodes were highly nonlinear.Our initial theoretical work centred around the search for exact solutions (by symmetry reduction) of a continuum model of NLTL. This investigation proved to be somewhat of a dead end and other continuum approximations highlighted in the literature assumed low amplitude pulses propagated along the line, which was not generally applicable in our case. Consequently we decided to look directly at the differential-difference equations which described the circuit and we have recently met with some success. Using Pad+ approximants we have obtained approximate analytical solutions to a practical NLTL, which we have fabricated in the electronic engineering laboratory. The obtained pulse measurements from the practical NLTL agreed well with our simulations and theoretical predictions. Our findings will be presented at a conference in Montpellier to be held from 21/2/95 to25/2/95.We are continuing our investigation into obtaining more accurate solutions of the transmission line equations and we are seeking to include the effects of dissipation into our theoretical models, in addition to deriving two and threes soliton solutions. As a result of our investigations we are hoping to fabricate a highly nonlinear transmission line with excellent pulse shortening properties using commercially available snap-recovery diodes.
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Organisation Website:	http://www.kent.ac.uk