浅水波的能量不变量和Korteweg-de Vries方程。能量总是不变量吗？
Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Is energy always an invariant?
摘要：
众所周知，KdV方程有无穷多个守恒量。前三个通常被认为代表质量、动量和能量。在这里，我们试图回答的问题，这是如何来的，以及如何这些KdV量与欧拉浅水方程。在这里，卢克的拉格朗日量是有帮助的。我们还考虑了KdV的高阶扩展。虽然在一般情况下不可积，但在某种意义上它们几乎可积。
英文摘要：
It is well known that the KdV equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum and energy. Here we try to answer the question of how this comes about, and also how these KdV quantities relate to those of the Euler shallow water equations. Here Luke's Lagrangian is helpful. We also consider higher order extensions of KdV. Though in general not integrable, in some sense they are almost so.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
