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首页> 外文期刊>Journal of Experimental and Theoretical Physics >The fermi-pasta-ulam recurrence and related phenomena for 1D shallow-water waves in a finite Basin~1
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The fermi-pasta-ulam recurrence and related phenomena for 1D shallow-water waves in a finite Basin~1

机译：有限盆地〜1中一维浅水波的费米-帕斯塔-乌拉姆复发及相关现象

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摘要

Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear "one-dimensional" potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.
机译：对于两个垂直壁之间有限深度的水槽中的完全非线性“一维”潜在水波，数值模拟了费米-帕斯塔-乌拉姆（FPU）递归的不同形式。在这样的系统中，FPU的重复与近似对应于可积Boussinesq系统的孤子的相干结构的动力学密切相关。 Boussinesq模型的一个最简单的周期解（描述了壁之间的一个孤子）以椭圆Jacobo函数的解析形式给出。在数值实验中，可以观察到，取决于水槽中孤子的数量及其参数，FPU的复发可能以简单或复杂的方式发生，或者实际上不存在。为了进行比较，模拟了非均匀河床​​上潜在水波的非线性动力学，初始状态采取了几对碰撞孤子的形式。具有缓坡的床剖面，在演化过程中的典型现象是出现了相对较高的（无赖）波，而对于随机，相对短相关的床剖面，则要么是高波出现，要么是尖锐的形成。在中等高度的波峰。

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