Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation

Abstract

We study the generalized hydrodynamics of the one-dimensional classical Non Linear Schroedinger equation in the attractive phase. We thereby show that the thermodynamic limit is entirely captured by solitonic modes and radiation is absent. Our results are derived by considering the semiclassical limit of the quantum Bose gas, where the Planck constant has a key role as a regulator of the classical soliton gas. We use our result to study adiabatic interaction changes from the repulsive to the attractive phase, observing soliton production and obtaining exact analytical results which are in excellent agreement with Monte Carlo simulations.

24 pages, 4 figures

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• Exact large-scale fluctuations of the phase field in the sine-Gordon model
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• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
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• Particle Scattering and Fusion for the Ablowitz-Ladik Chain
• Quantum fluctuating theory for one-dimensional shock waves
• Observation of a generalized Gibbs ensemble in photonics
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas