NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	NORTH DAKOTA STATE UNIVERSITY
Initial Amendment Date:	June 15, 1992
Latest Amendment Date:	June 15, 1992
Award Number:	9217627
Award Instrument:	Standard Grant
Program Manager:	DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 1992
End Date:	December 31, 1995 (Estimated)
Total Intended Award Amount:	$61,425.00
Total Awarded Amount to Date:	$61,425.00
Funds Obligated to Date:	FY 1992 = $61,425.00
History of Investigator:	Tuncay Aktosun (Principal Investigator) aktosun@uta.edu
Recipient Sponsored Research Office:	North Dakota State University Fargo 1340 ADMINISTRATION AVE FARGO ND  US  58105 (701)231-8045
Sponsor Congressional District:	00
Primary Place of Performance:	DATA NOT AVAILABLE
Primary Place of Performance Congressional District:
Unique Entity Identifier (UEI):	EZ4WPGRE1RD5
Parent UEI:	EZ4WPGRE1RD5
NSF Program(s):	APPLIED MATHEMATICS
Primary Program Source:
Program Reference Code(s):	9229
Program Element Code(s):	126600
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

This project consists of an investigation of the inverse scattering problems for the multidimensional Schrodinger equations when the potential is independent of energy and when the potential is proportional to energy. In the former case, the Wiener-Hopf factorization and the generalized Muskhelishvili- Vekua technique will be used to investigate the characterization of the scattering data, the relationship between bound states and partial indices, the inversion from partial data, and the stability of the inversion. In the latter case, the inverse scattering problem will be formulated as a Riemann-Hilbert problem with a discontinuity of almost periodic type and its solution will be obtained through a generalized Wiener-Hopf factorization technique. The solution of the inverse scattering problem with energy- independent potentials is equivalent to determining molecular, atomic, and nuclear forces in terms of the scattering data obtained in collision experiments, and the determination of these forces is one of the fundamental problems in physics. The inverse scattering problem with energy-dependent potentials is equivalent to the determination of the properties of a medium using only the measurements made on the boundary; such a problem has many important applications in wave propagation, seismology, nondestructive testing, oil exploration, atmospheric profile inversion, and other areas.

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