Nonlinear Effects and Run-up of Coastal Waves Generated by Billiards with Semi-rigid Walls in the Framework of Shallow Water Theory

Pub Date : 2023-12-20 DOI:10.1134/s0081543823040090

S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova

引用次数: 0

Abstract

By coastal waves we mean time-periodic or nearly time-periodic gravity waves on water in a basin of depth \(D(x)\), \(x=(x_1,x_2)\), that are localized in the vicinity of the coastline \(\Gamma^0=\{D(x)=0\}\). In this paper, for the system of nonlinear shallow water equations, we construct asymptotic solutions corresponding to coastal waves in two specific examples. The solutions are presented in the form of parametrically defined functions corresponding to asymptotic solutions of the linearized system, which, in turn, are related to the asymptotic eigenfunctions of the operator \(-\nabla\cdot (g D(x)\nabla)\) that are generated by billiards with semi-rigid walls.

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浅水理论框架下带有半刚性壁的台球产生的海岸波的非线性效应和上升趋势

Abstract by coastal waves we mean time-periodic or nearly time-periodic gravity waves on water in a basin of depth \(D(x)\), \(x=(x_1,x_2)\), that are localized in the vicinity of the coastline \(\Gamma^0=\{D(x)=0\}\)。本文针对非线性浅水方程系统，在两个具体例子中构建了与海岸波相对应的渐近解。这些解以参数定义函数的形式呈现，这些函数与线性化系统的渐近解相对应，而线性化系统的渐近解又与具有半刚性壁的台球产生的算子 \(-\nabla\cdot (g D(x)\nabla)\) 的渐近特征函数相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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