Mathematical Sciences: Development and Applications of Periodic Soliton Theory for Nearly Integrable P.D.E.

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This project focuses on the investigation of mathematical models of nonlinear wave phenomena such as the appearance and persistence of large eddies and the onset of turbulence in fluid flow. The formation and oscillation of coherent structures are phenomena which such as the Kuramoto-Sivashinisky, Sine-Gordon and Nonlinear Schroedinger equations. By employing methods of inverse spectral theory, invariant manifold theory and numerical methods, this project will be aimed at explaining the common mechanism which gives rise to the above phenomena in these disparate models.