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On spectral theory of soliton and breather gases for integrable equations

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

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 surface combined with simultaneous (exponentially fast in N) shrinking  of the bands. We present recent results on  the average densities and fluxes of solution gases, on the thermodynamic limit of quasimomentum and quasienergy differentials and introduce and discuss periodic soliton gases.

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

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