The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial conditions. A similarly powerful approach has recently emerged that is applicable to quantum integrable systems, namely the generalized hydrodynamics approach. This paper aims at showing that the Whitham approach is the semiclassical limit of the generalized hydrodynamics approach by connecting the two formal methods explicitly on the example of the Lieb–Liniger model on the quantum side to the non-linear Schrödinger equation on the classical side in the c → 0 limit, c being the interaction parameter. We show how quantum expectation values may be computed in this limit based on the connection established here which is mentioned above.

中文翻译：

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Whitham方法到达Lieb–Liniger模型的c→0极限和广义流体动力学

Whitham方法是描述非线性可积系统的一种经过充分研究的方法。尽管本质上是近似的，但是其结果可以在给定初始条件的情况下相当准确地预测此类系统的时间演变。最近出现了一种适用于量子可积系统的类似有效方法，即广义流体力学方法。本文旨在通过将量子侧的Lieb–Liniger模型示例中的两种形式方法与经典侧的非线性Schrödinger方程显式连接，来证明Whitham方法是广义流体力学方法的半经典极限。 c→0极限，c是交互参数。