# Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation

@inproceedings{Spohn2021HydrodynamicEF, title={Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation}, author={Herbert Spohn}, year={2021} }

Ablowitz and Ladik discovered a discretization which preserves the integrability of the nonlinear Schrödinger equation in one dimension. We compute the generalized free energy of this model and determine the GGE averaged fields and their currents. They are linked to the mean-field circular unitary matrix ensemble (CUE). The resulting hydrodynamic equations follow the pattern already known from other integrable many-body systems. Studied is also the discretized modified Korteweg-de-Vries…

## 2 Citations

Inverse scattering solution of the weak noise theory of the Kardar-Parisi-Zhang equation with flat and Brownian initial conditions

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We present the solution of the weak noise theory (WNT) for the Kardar-Parisi-Zhang equation in one dimension at short time for flat initial condition (IC). The non-linear hydrodynamic equations of…

Large Deviations for Ablowitz-Ladik lattice, and the Schur flow

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We consider the Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, and the Schur flow. We derive large deviations principles for the distribution of the empirical measures of the equilibrium…

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