Mathematical Sciences: Coherence and Chaos in PDE's and     Nonlinear Wave Propagation
{'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}
This project involves research on nonlinear dynamical systems               exhibiting wave phenomena. It has two main goals: (1) to understand to          what extent the chaotic behavior in partial differential equations is           finite dimensional; (2) to study a variety of propagation phenomena.            Under goal (1) the                                                              investigations will focus on two kinds of systems described by partial          differential equations: nearly integrable systems described by forced           damped nonlinear Schrodinger equation and by sine-Gordon equation. They         are natural extensions into PDE's of forced damped pendulum, a problem          used as a prototype for studying chaos in ordinary differential                 equations. These equations have a natural choice of a basis, with which         the notion of a nonlinear power spectrum can be described explicitly for        the first time. The near integrability of these equations provides              sufficient analytical control to yield precise, detailed theoretical            information about the qualitative behavior. The far from integrable             systems include flows in finite geometries, turbulent wakes and boundary        layers. Here the issue is to find an optimal decomposition of the flow          field for which the dimension of the subspace of modes which dominate           the dynamics is minimal.                                                            Under goal (2), the propagation of nonlinear waves will be studied          in a variety of contexts, trying to answer questions such as the                existence of Anderson localization in nonlinear waves propagating in a          random medium, theoretical foundations of nonlinear optics, and                 mathematical theory of singularities of envelope equations.                         This research is part of a larger effort in the nonlinear analysis          of dynamical systems which has been developed in this country in the            last ten years. Studies like this are important for a deep understanding        of a number of nonlinear phenomena in the existing dynamical systems            encountered in technology.
[{'FirstName': 'Martin', 'LastName': 'Casdagli', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Martin C Casdagli', 'EmailAddress': None, 'NSF_ID': '000000018', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Alan', 'LastName': 'Newell', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Alan C Newell', 'EmailAddress': 'anewell@math.arizona.edu', 'NSF_ID': '000102201', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Nicholas', 'LastName': 'Ercolani', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Nicholas M Ercolani', 'EmailAddress': 'ercolani@math.arizona.edu', 'NSF_ID': '000227147', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'David', 'LastName': 'McLaughlin', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'David W McLaughlin', 'EmailAddress': 'david.mclaughlin@nyu.edu', 'NSF_ID': '000387620', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}]
{'Name': 'University of Arizona', 'CityName': 'TUCSON', 'ZipCode': '85721', 'PhoneNumber': '5206266000', 'StreetAddress': '845 N PARK AVE RM 538', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arizona', 'StateCode': 'AZ', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'AZ07', 'ORG_UEI_NUM': 'ED44Y3W6P7B9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ARIZONA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126600', 'Text': 'APPLIED MATHEMATICS'}
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