Mathematical Sciences: Nonlinear Waves: Theory and          Computation
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{'SignBlockName': 'Alvin I. Thaler', 'PO_EMAI': None, 'PO_PHON': None}
Nonlinear phenomena are important across all of science.                They constitute a broad and poorly understood area which draws on               a diverse range of mathematical disciplines.  This research                     program addresses to an area of nonlinear analysis which has                    recently shown considerable progress:  nonlinear waves in                       hyperbolic systems and in coupled hyperbolic-elliptic systems.                  The investigators intend to develop computational methods which                 are based on this mathematical theory and to participate in the                 development of the mathematical theory of these waves.                                  The goal of this work is to develop the mathematical theory             and to utilize it to the maximum extent possible within the                     computational process.  The success of front tracking shows that                this goal is attainable.  One of the investigator's major                       accomplishments has been the proof of scientific principle for                  the front tracking method.  This method is now accepted, on the                 basis of evidence developed within the research program.  The                   success of front tracking has been confirmed by independent work                of others.  It parallels in two dimensions the previous success                 which has been achieved by the Random Choice Method in one                      dimension.  The development and use of mathematical theory in the               computational process was likewise a characteristic feature of                  the Random Choice Method.
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