KdV与BBM方程孤立波完全相互作用近似解析研究  

Analytical study on the interaction of solitary waves between KdV and BBM equation

作　　者：尤翔程[1] 刘曾 崔继峰[3] YOU Xiang-cheng;LIU Zeng;CUI Ji-feng(College of Petroleum Engineering,China University of Petroleum-Bey ing,Beijing 102249,China;School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;College of Sciences,Inner Mongolia University of Technology,Hohhot,010051)

机构地区：[1]中国石油大学(北京)石油工程学院,北京102249 [2]华中科技大学船舶与海洋工程学院,湖北武汉430074 [3]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《舰船科学技术》2022年第5期76-79,共4页Ship Science and Technology

基　　金：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)。

摘　　要：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.

关 键 词：KDV方程 BBM方程 孤立波 相互作用 守恒量 

分 类 号：TP139.2[自动化与计算机技术—控制理论与控制工程]