These are lecture notes for a series of lectures given at the Les Houches Summer School on
Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same …

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

Soliton gases represent large random soliton ensembles in physical systems that exhibit
integrable dynamics at the leading order. Despite significant theoretical developments and …

We investigate the fundamental phenomenon of the spontaneous, noise-induced
modulational instability (MI) of a plane wave. The statistical properties of the noise-induced …

Breathers or oscillating wave packets, along with solitons, are the most energy-carrying
waves in various physical media, ie surface and internal waves, optical networks, and …

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 …

We report on an experimental realization of a bidirectional soliton gas in a 34-m-long wave
flume in a shallow water regime. We take advantage of the fission of a sinusoidal wave to …

A bstract We provide a simple geometric meaning for deformations of so-called\(T\overline
{T}\) type in relativistic and non-relativistic systems. Deformations by the cross products of …

Solitons and breathers are localized solutions of integrable systems that can be viewed as
“particles” of complex statistical objects called soliton and breather gases. In view of the …