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Spectral asymptotics of Zahkarov Shabat operators and their application to the nonlinear Schrdinger equation on the circle

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Periodic and Ergodic Spectral Problems

In this talk I will present asymptotics of various spectral quantities of Zahkarov Shabat operators and show how to apply them for proving that the nonlinear Fourier transform of the defocusing nonlinear Schrdinger equation on the circle (Birkhoff map)is the linear Fourier transform up to a nonlinear part which is 1-smoothing.Various implications will be discussed. This is joint work with Beat Schaad and Peter Topalov.

This talk is part of the Isaac Newton Institute Seminar Series series.

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