Generalized hydrodynamics of the attractive non-linear Schrödinger equation. (English) Zbl 1507.35258
Summary: We study the generalized hydrodynamics of the one-dimensional classical non linear Schrödinger 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
Keywords:
generalized hydrodynamics; attractive non-linear Schrödinger; adiabatic interaction changes; integrabilityReferences:
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