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Seminar

On a class of perturbations of the special pole-free joint solution of KdV and PI2 under the action of the KdV flow

by Alexander Minakov (UCLouvain)

Location: CYCL09b, Louvain-la-Neuve
Time: Thursday October 18, 2018 at 15:00

We consider perturbations of the special pole-free joint solution U(x,t) of the Korteweg-de Vries equation ut+uux+112uxxx=0 and P2I equation uxxxx+10u2x+20uuxx+40(u36tu+6x)=0 under the action of the KdV flow. We show that if the perturbation is compact and of bounded variation, then the initial value problem for the KdV equation has a classical solution. Our method is the inverse scattering transform method in the form of the Riemann-Hilbert problem method. Namely, we construct the corresponding spectral functions a(λ),r(λ), and give characterization of the compact perturbations in terms of a(λ),r(λ). This is a joint work in progress with B. Dubrovin.

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