NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	RUTGERS, THE STATE UNIVERSITY
Initial Amendment Date:	May 29, 2001
Latest Amendment Date:	August 4, 2003
Award Number:	0100490
Award Instrument:	Continuing Grant
Program Manager:	Joe W. Jenkins DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	June 1, 2001
End Date:	May 31, 2005 (Estimated)
Total Intended Award Amount:	$126,002.00
Total Awarded Amount to Date:	$152,524.00
Funds Obligated to Date:	FY 2001 = $42,000.00 FY 2002 = $42,001.00 FY 2003 = $68,523.00
History of Investigator:	Avraham Soffer (Principal Investigator) soffer@math.rutgers.edu
Recipient Sponsored Research Office:	Rutgers University New Brunswick 3 RUTGERS PLZ NEW BRUNSWICK NJ  US  08901-8559 (848)932-0150
Sponsor Congressional District:	12
Primary Place of Performance:	Rutgers University New Brunswick 3 RUTGERS PLZ NEW BRUNSWICK NJ  US  08901-8559
Primary Place of Performance Congressional District:	12
Unique Entity Identifier (UEI):	M1LVPE5GLSD9
Parent UEI:
NSF Program(s):	ANALYSIS PROGRAM
Primary Program Source:	01000102DB NSF RESEARCH & RELATED ACTIVIT app-0102  app-0103
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

There are two main topics of research in this proposal, first, the
large time behaviour and scattering theory of nonlinear Schrodinger
waves off a potential term which supports many bound states. This leads
to the analysis of multichannel nonlinear scattering and metastability
of hamiltonian dispersive equations. The second topic involves the study of
radiation damping for metastable mutltibreather solutions of the wave
equation. The large time behaviour of the linearized wave equation around
multibreather solutions is analyzed; a theory to estimate the lifetimes
of perturbed multibreather solutions is developed and applications
to nonlinear optics, in particular optical guides with non-uniform diffraction
profiles.

The use of optical devices and fibers in today's communication systems
motivates some of the problems studied in this proposal. In particular
we concentrate on the problem of effects of defects and other irregularities
in optical fibers on their transport properties. We also analyze some
novel optical devices made by modifying the medium in a way to achieve
better filtering of noise and interchannel interference.

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