Abstract: Soliton gases for integrable systems is a rapidly developing new area in the theory of nonlinear waves. The spectral theory of soliton gases is concerned about macroscopic characteristics of large soliton ensembles. We go briefly over the history of the subject, such as V. Zakharov’s (1971) expression of the average velocity of a trial soliton in a (diluted) gas and the idea of the thermodynamic limit of wavenumbers and frequencies of finite gap solutions of G. El (2003). We then discuss some recent results and open problems, as well as some methods of potential theory and algebraic geometry that appear to be relevant for soliton gases.

Contact: Peter Miller