Alexander Tovbis

On spectral theory of soliton gases for integrable equations

Considering 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 surfaces combined with simultaneous (exponentially fast in N) shrinking of the bands. We discuss recent developments of the theory, including the average densities and fluxes of soliton gases, the thermodynamic limit of quasimomenta and quasienergy differentials, periodic soliton gases, etc.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/9ee8a8facac6428587a6fb6c1201b23e1d