Description
The concept of a soliton gas was introduced by V. Zakharov
in 1971 and further extended by G. El. The physical intuition is that the dispersive dynamic of a strongly nonlinear and integrable random field is dominated by solitons interactions. A deterministic model for such fields involves the idea of a primitive potential as a condensation of many solitons. On the other hand, the kinetic theory of solitons is rapidly booming and makes strong connections with the theory of dispersive hydrodynamics, originally developed by Whitham and the theory of generalized hydrodynamics that has emerged recently to describe the non-equilibrium physics of integrable systems where the extensive amount of ballistic transport renders conventional theories inapplicable. These lectures will survey both the deterministic and
kinetic approaches to soliton gases.