论文标题
水波：非线性理论
Water Waves: Nonlinear Theory
论文作者
论文摘要
提出了深水中表面重力波的一种新型的数学非线性理论，其中对流体动力学的经典非线性方程的分析分析在限制性的假设下进行的，而不是现有理论所应用的假设。特别是，新理论可确保解决方案的独特性无需采用所谓的辐射条件，其解决方案使液体始终保持在无穷大的静止状态，并且通过扰动来源提供给水的能量始终是有限的 - 与在空间内无限制的Harmonic Waves相反，所有这些都与常规方法相反。新理论解释了问题的非线性，并始终有效地产生解决方案，从零（设定初始条件的时间）到无穷大。作者描述了以前的波化中未知模式，并通过其他研究人员的实验结果证实了这些模式。
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those applied by existing theories. In particular, the new theory ensures uniqueness of the solution without the need to employ the so-called radiation condition, and its solutions are such that the liquid always remains at rest at infinity, and the energy supplied to the water by a source of disturbances is finite at all times - all that in contrast with conventional approaches that operate in terms of spatially-infinite harmonic waves. The new theory accounts for the non-linearity of the problem, and yields solutions valid at all times, from zero (the time of setting initial conditions) to infinity. The author describes previously unknown patterns in wave evolution, and confirms those patterns with the experimental results by other researchers.
