Mathematical Sciences: Waves in Nonlinear Dispersive and    Hyperbolic Systems
{'Code': '03040101', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Alan Izenman'}
This ongoing research program on nonlinear waves will                   focus on the following three topics:                                                    1. Functional path integrals.                                                   2. Exact modulation.                                                            3. Three wave resonant interactions.                                    The first two topics are concerned with the study of some                       relationships among equations with the Painleve property, equations             solvable by the Inverse Scattering Transform method, the theory of              wave modulation and representation of solution                                  of partial differential equations by path integrals. The                        last topic is concerned with the study of weakly nonlinear                      interactions of waves in strictly hyperbolic systems.                                   The mathematical theory of nonlinear waves is a mathema-                tical model of physical wave propagation.  The conclusions                      deduced from the theory are generally useful to our under-                      standing of many natural and technological phenomena.  The present              research program on nonlinear waves is aimed toward                             a better understanding of resonance and instability which                       are causes for failures in structural and fluid systems.  The                   research results are expected to contribute to better designs                   for many such engineereing systems.
{'FirstName': 'Rodolfo', 'LastName': 'Rosales', 'EmailAddress': 'rrr@math.mit.edu', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8702625.xml'}