Graduate Student / Postdoc Seminar

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Modified Scattering for the Modified Korteweg-De Vries Equation (mKdV)

Speaker: Benjamin Harrop-Griffiths

Location: Warren Weaver Hall 1302

Date: Friday, November 6, 2015, 1 p.m.

Synopsis:

The Korteweg-de Vries (KdV) equation arises as an asymptotic limit of numerous dispersive systems and together with its generalizations has a wide range of physical applications including fluid mechanics, plasma physics and nonlinear optics. In this talk we will provide a brief introduction to the generalized KdV family of equations with particular emphasis on their asymptotic behavior. In particular we will discuss why solutions to the modified KdV (mKdV) do not scatter to linear waves, even for small initial data and will sketch a proof of modified scattering using the method of testing by wave packets. This robust approach does not rely on the inverse scattering transform and hence may be applied to short range perturbations of the mKdV as well as numerous other non-integrable equations.