We review the spectral theory of soliton gases in integrable dispersive hydrodynamic
systems. We first present a phenomenological approach based on the consideration of …

We introduce and study a novel class of classical integrable many-body systems obtained
by generalized TT¯ deformations of free particles. Deformation terms are bilinears in …

We introduce a new universal framework describing fluctuations and correlations in
quantum and classical many-body systems, at the Euler hydrodynamic scale of space and …

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of
weakly interacting solitons in the framework of Korteweg–de Vries (KdV) equation. In this …

The theory of soliton gas had been previously developed for unidirectional integrable
dispersive hydrodynamics in which the soliton gas properties are determined by the …

The lecture notes cover the emergence of generalized hydrodynamics for the classical and
quantum Toda chain, the classical Calogero fluid, the Ablowitz-Ladik discretization of the …

We consider a generalized Gibbs ensemble of the classical Toda lattice. We establish that
the collision rate ansatz follows because (i) the charge-current susceptibility matrix is …

1. Introduction, 2. Dynamics of the classical Toda lattice, 3. Static properties, 4. Mean-field
Dyson Brownian motion, 5. Hydrodynamics for hard rods, 6. Generalized hydrodynamic …

Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one
generic approach we develop form factor expansions, for ground states and generalized …

We construct an integrable lattice model of classical interacting spins in discrete space-time,
representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with …