Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation

  title={Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schr{\"o}dinger equation},
  author={Herbert Spohn},
  journal={Journal of Mathematical Physics},
  • H. Spohn
  • Published 10 July 2021
  • Mathematics
  • Journal of Mathematical Physics
Ablowitz and Ladik discovered a discretization that preserves the integrability of the nonlinear Schrödinger equation in one dimension. We compute the generalized free energy of this model and determine the generalized Gibbs ensemble averaged fields and their currents. They are linked to the mean-field circular unitary matrix ensemble. The resulting hydrodynamic equations follow the pattern already known from other integrable many-body systems. The discretized modified Korteweg–de-Vries… 
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