Generalized hydrodynamics for the Volterra lattice: ballistic and non-ballistic behavior of correlation functions

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Lattice dynamics; integrable lattice equations (37K60) Integrable difference and lattice equations; integrability tests (39A36)

Cites Work

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Kinetic equation for a soliton gas and Its hydrodynamic reductions
Three integrable Hamiltonian systems connected with isospectral deformations
On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
The thermodynamic limit of the Whitham equations
Correlation functions for a chain of short range oscillators
Rigorous asymptotics of a KdV soliton gas
Discrete integrable systems and random Lax matrices
Large deviations for Gibbs ensembles of the classical Toda chain
Generalized Gibbs ensembles of the classical Toda chain
Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit
A large deviation principle for empirical measures on Polish spaces: application to singular Gibbs measures on manifolds
An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit
On the Toda Lattice. II: Inverse-Scattering Solution
Matrix models for beta ensembles
The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain
Generalized hydrodynamics of the attractive non-linear Schrӧdinger equation
Kinetic theory of quantum and classical Toda lattices
Ballistic space-time correlators of the classical toda lattice
Generalized hydrodynamics of the classical Toda system
Tridiagonal realization of the antisymmetric Gaussian β-ensemble
Soliton gas in integrable dispersive hydrodynamics
Generalized hydrodynamics of the KdV soliton gas
On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice
Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation
Equilibrium spacetime correlations of the Toda lattice on the hydrodynamic scale
Large deviations for Ablowitz-Ladik lattice, and the Schur flow
Exact thermodynamics and transport in the classical sine-Gordon model

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