Nonlinear Evolution Equations

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NONLINEAR EVOLUTION EQUATIONSAbstract of Proposed ResearchGustavo Ponce This project is devoted to research into various aspects of nonlinear dispersive equations. It will include work on several nonlinear dispersive evolution equations of Schroedinger type. These arise as approximate models for the evolution of vortex filaments, in water waves modeling and as examples of higher order integrable systems. Also some unique continuation properties of nonlinear dispersive models will be investigated. The goal is to use these properties to established uniqueness of solutions to an associated problem from some incomplete information of the solutions at two different times.They problems to be investigated are at the intersection of partial differential equations, classical harmonic analysis and mathematical physics. The unique continuation issues arise naturally in control theory applications.