Mathematical Sciences: Phase Shift Phenomenon for Perturbed Evolution Equations and Applications to Nonlinear Optics

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9626672 Alber In this project methods of symplectic geometry and geometric mechanics are to be used to analyze the phase-space geometry of nonlinear wave systems and to investigate new techniques for soliton perturbation theory. In particular, the investigator plans to study geometric and Maslov phases of nonlinear wave systems and a KAM type theory for dynamical systems with phase spaces foliated by the nonlinear compact invariant varieties. Geometric mechanics reformulates parts of classical mechanics using the modern language of symplectic differential geometry. It has potential applications in a variety of applications including locomotion generation, motion control and nonlinear optics.