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Recent Developments in Spectral Theory of Focusing NLS Soliton Gases: Average Densities, Fluxes and Periodic Gases

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HY2W02 - Analysis of dispersive systems

In this talk, we will discuss soliton and breather gases for one-dimensional integrable focusing Nonlinear Schrödinger Equation (fNLS). The derivation of average densities and fluxes for such gases will be presented. Thermodynamic limits of quasimomentum, quasienergy, and their connections with the corresponding g-functions will also be discussed. We then introduce the notion of periodic fNLS gases and calculate for them the average densities, fluxes and thermodynamic limits of meromorphic differentials, including error estimation. Our results constitute another step towards the mathematical foundation for the spectral theory of fNLS soliton and breather gases that appeared in the work of G. El and A. Tovbis, Phys. Rev. E, 2020. (This is joint work with Alexander Tovbis)

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

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