Shabat spectra and a minimal Dirichlet energy problem

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• Marco Bertola (Concordia University)
• Tuesday 23 July 2024, 15:00-16:00
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PDW - Emergent phenomena in nonlinear dispersive waves

In this talk (joint work with A. Tovbis) I will discuss the spectra of finite-gap solutions for fNLS.  We will show that the average intensity is equivalent to a problem in harmonic analysis of computing a specific Dirichlet energy associated with a domain in the upper half plane. We will also show that the Zakharov-Shabat spectra of finite gap solutions realize (local) minima of these Dirichlet energies amongst a well defined class of compact sets, a result that suggests a local stability property. Some elements of the proof will be discussed. 

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

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