University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On spectral theory of soliton gases for integrable equations, Part 1: Brief introduction. Part 1

On spectral theory of soliton gases for integrable equations, Part 1: Brief introduction. Part 1

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Taking the focusing NLS as a model example, we introduce soliton gas through the thermodynamic limit of multi-phase (finite gap) solutions. This limit can be characterized by the growing genus 2N  of the corresponding hyperelliptic Riemann surface  combined with simultaneous (exponentially fast in N) shrinking  of the bands. We then derive the Nonlinear Dispersion Relations, introduce  important classes of soliton gases, such as soliton condensates, and discuss some examples.  

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

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