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Degenerate Dispersive PDE and Nonlinear Schrödinger Equations

Student-Run Applied & Math Seminar

Speaker: Evan Smothers, UC Davis Mathematics
Location: 2112 MSB
Start time: Wed, Jan 25 2017, 12:10PM

Nonlinear Schrödinger equations model a wide range of physical phenomena, from the propagation of waves in fiber optics to the evolution of slowly varying water waves. They are also a prime example of a dispersive PDE. Degenerate dispersive equations are those PDE in which dispersive effects may vanish depending on properties of the solution (for instance when the solution itself vanishes), making existence results more difficult to obtain. I'll give some background in both these areas (with plenty of examples), introduce a nonlinear Schrödinger equation exhibiting degenerate dispersion, and discuss some results regarding this particular equation.