Chapter 1: Overview
Chapter 2: Dynamics of the Classical Toda Lattice
Chapter 3: Static Properties
Chapter 4: Dyson Brownian Motion
Chapter 5: Hydrodynamics for Hard Rods
Chapter 6: Equations of Generalized Hydrodynamics
Chapter 7: Linearized Hydrodynamics and GGE Spacetime Correlations
Chapter 8: Domain Wall Initial States
Chapter 9: Toda Fluid
Chapter 10: Hydrodynamics of Soliton Gases
Chapter 11: Calogero Models
Chapter 12: Discretized Nonlinear Schrödinger Equation
Chapter 13: Hydrodynamics for the Lieb–Liniger δ-Bose Gas
Chapter 14: Quantum Toda Lattice
Chapter 15: Beyond the Euler Time Scale

This book provides a broad introduction to integrable systems with many degrees of freedom. Within a much larger orbit, discussed are models such as the classical Toda lattice, Calogero fluid, and Ablowitz-Ladik discretized nonlinear Schrödinger equation. On the quantum mechanical side, featured are the Lieb-Liniger delta-Bose gas and the quantum Toda lattice. As a genuinely novel twist, the study deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, in spirit similar to the ballistic Euler scale of nonintegrable simple fluids. While integrable microscopic particle models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales.---summary provided by publisher