Mathematical Sciences: Nonlinear Dispersive Waves

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This project will support research in the area of nonlinear dispersive systems, in particular, the nonlinear Schrodinger equation and the Zakharov equation. The research will be focused in four areas: (1) nonlinear scattering and stability, (2) singularity formation and nucleation for the nonlinear Schrodinger equation and Zakharov systems, (3) dispersion of low energy solutions of equations arising in the mathematical description of the propagation of long waves, and (4) parametric resonance in Hamiltonian systems and the effect of dissipation. Nonlinear wave phenomena arise in physical systems ranging from the quantum level to the large scale motion of fluids in oceans. Problems in nonlinear waves can be studied using various techniques: analytical, formal asymptotics, and computer simulations.