Mathematical Sciences: Analysis of Solitary Wave Phenomena

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This project shall concentrate on the analysis of solitary wave phenomena. Several related questions in the analysis of solitary waves will be examined, including their existence, uniqueness and stability. In addition, the validity of various approximate equations and certain rigorous properties of nonlinear dispersive systems of partial differential or integro- differential equations will be considered. The tools of nonlinear analysis will be supplemented by some numerical simulation and the special methods of inverse scattering theory. The systems to be studied arise in many areas of nonlinear science including fluid mechanics, nonlinear optics, solid state physics, oceanography and meteorology.