Mathematical Sciences: Nonlinear Waves
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This work will emphasize new mathematical directions in the                treatment of nonlinear wave equations in which geometry and                     dynamical systems play a significant role in the qualitative                    theory.  The general theme of the work is to analyze singularity                formation and stability properties for nonlinear equations                      arising in geometry and physics (particle field theory in                       particular).                                                                         One particular objective is to continue studies on the                     nonlinear sigma model described by nonlinear maps from Minkowski                space to complete Riemannian manifolds.  The mathematical                       interest in these models is centered on the existence of                        solutions defined on all space-time and the development of                      singularities.  Local existence results are known, and in higher                dimensions solutions with small initial data can be shown to                    exist for all time.  Recent results show that weak solutions with               initial data of any (finite energy) for restricted target                       manifolds.  Work will now be done in an effort to relax this                    condition.                                                                           A second line of investigation focuses on the classification               of differential equations close to critical points as first                     developed by Poincare.  The fundamental problem is that of                      establishing analytic transformations which conjugate equations                 into linear ones.  In the ordinary differential equations case,                 the answers lie in the nature of the spectrum (resonance).  For                 partial differential equations the situation is different,                      although some positive results are available.  Work will                        continue toward the establishment of both analytic and                          nonanalytic transformations for nonlinear Schrodinger equations.
{'FirstName': 'Jalal', 'LastName': 'Shatah', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jalal Shatah', 'EmailAddress': 'shatah@cims.nyu.edu', 'NSF_ID': '000369372', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'New York University', 'CityName': 'NEW YORK', 'ZipCode': '100121019', 'PhoneNumber': '2129982121', 'StreetAddress': '70 WASHINGTON SQ S', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'NY10', 'ORG_UEI_NUM': 'NX9PXMKW5KW8', 'ORG_LGL_BUS_NAME': 'NEW YORK UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8802614.xml'}