Inverse Scattering in 60 Minutes

Perry, Peter

Journées équations aux dérivées partielles (2016), Exposé no. 8, 17 p.

This lecture reports on joint work with Robert Jenkins, Jiaqi Liu, and Catherine Sulem. We illustrate the strengths of the inverse scattering method for addressing large-time behavior of completely integrable dispersive PDE’s by proving global well-posedness and determining large-time asymptotic behavior for the Derivative Nonlinear Schrödinger equation (DNLS) for soliton-free initial data. Our work uses techniques from the work of Deift and Zhou on the defocussing NLS together with further developments due to Dieng and McLaughlin.

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