本文使用了质量、动量和能量守恒量，对KdV方程和BBM方程两孤立波完全相互作用特性进行近似解析和数值研究，应用守恒量等式计算合并波形，无需求解相关的非线性偏微分方程。综合比较了KdV方程和BBM方程的数值计算结果以及近似合并波形解析结果，使用守恒量近似分析方法研究两孤立波相互作用，可以用较小的计算量获得各种有用的计算结果。研究表明，该方法具有较好的工程近似精度，可适用于预测波浪与海洋、海岸和运河结构物等相互作用情况。
This paper uses the conserved quantities of mass, momentum and energy to approximate and analytically study the complete interaction of solitary waves in KdV equation and BBM equation. The conserved quantities are applied to calculate the merged wave without solving nonlinear partial differential equations. The numerical results of KdV equation and BBM equation and the analytical results of approximate merged wave are comprehensively compared. It is considered that using the conserved quantities to study the solitary wave interaction has a good approximate analytical model and a small amount of calculation. The results show that this method has good engineering approximation accuracy and maybe suitable for predicting the interaction between waves and ocean, coastal and canal structures.
2022,44(5): 76-79 收稿日期：2021-11-19
DOI：10.3404/j.issn.1672-7649.2022.05.015
分类号：TP139.2
基金项目：国家自然科学基金资助项目（12002390；12072126；12062018；12172333）；内蒙古自然科学基金资助项目（No.2020MS01015）；内蒙古自治区高等学校青年科技英才支持计划资助项目（NJYT22075）
作者简介：尤翔程(1981?)，女，博士，讲师，研究方向为流体传热及非线性波浪
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