非线性Schroedinger方程的Ablowitz-Ladik离散的流体动力学方程
Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
摘要：
Ablowitz和Ladik发现了一种离散化方法，该方法保持了一维非线性薛定谔方程的可积性。我们计算了该模型的广义自由能，并确定了GGE平均场和电流。它们被链接到平均场圆形酉矩阵系综（CUE）。由此产生的流体动力学方程遵循的模式已经从其他可积多体系统。还研究了离散化的修正Korteweg-de-Vries方程，该方程与β Jacobi测井气体有关。
英文摘要：
Ablowitz and Ladik discovered a discretization which preserves the integrability of the nonlinear Schroedinger equation in one dimension. We compute the generalized free energy of this model and determine the GGE averaged fields and 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 equation which turns out to be related to the beta Jacobi log gas.
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