Mathematical Sciences: Nonlinear Oscillations/Completely    Integrable Systems
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
Professor Venakides intends to study mathematical problems of               oscillation and wave propagation.  He wants to determine the nature of          oscillations in waveforms which are governed by a nonlinear partial             differential equation of Schrodinger type.  The interesting part of this        work consists of studying the passage to the limit when the dispersive          term becomes very small.  Problems of this type were studied for the            Korteweg-DeVries equation by Peter Lax, Henry McKean and Eugene                 Trubowitz of Courant Institute and by Herman Flaschka and others from           the University of Arizona.  Venakides brings new techniques to his study        and wants to derive an integral equation which would characterize the           solution in the limit case.  He also wants to perform a similar study           for a system of nonlinear ordinary differential equations known as Toda         Lattice.  Other projects described by him include an inverse problem for        a Schrodinger equation, study of equations of granular flow and the work        on the understanding of certain procedure for stochastic equations with         a nonlinear operator.                                                               This research falls into the general area of studies in nonlinear           partial differential equations which describe wave propagation phenomena        such as solitary waves, acoustic waves, shocks and wavefronts, optical          communications and laser technology. This particular research is                intended to add to the knowledge base underlying such physical                  phenomena.                                                                              The nonlinear partial differential equations of the type                investigated in this project are important mathematical tools for               engineering problems encountered in wave propogation.
{'FirstName': 'Stephanos', 'LastName': 'Venakides', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Stephanos Venakides', 'EmailAddress': 'ven@math.duke.edu', 'NSF_ID': '000233856', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Duke University', 'CityName': 'DURHAM', 'ZipCode': '277054640', 'PhoneNumber': '9196843030', 'StreetAddress': '2200 W MAIN ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'North Carolina', 'StateCode': 'NC', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'NC04', 'ORG_UEI_NUM': 'TP7EK8DZV6N5', 'ORG_LGL_BUS_NAME': 'DUKE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
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