变系数KdV方程在海洋内孤立波的应用  

Application of Variable Coefficient KdV Equation to Solitary Waves in the Ocean

作　　者：陈万坤 袁春鑫 CHEN Wan-Kun;YUAN Chun-Xin(School of Mathematics and Physics,Qingdao University of Science and Technology, Qingdao 266061,China;School of Mathematics and Sciences, Ocean University of China, Qingdao 266100,China;School of Mathematics and Statistics,Heze University, Heze 274000,China)

机构地区：[1]青岛科技大学数理学院,山东青岛266061 [2]中国海洋大学数学与科学学院,山东青岛266100 [3]菏泽学院数学与统计学院,山东菏泽274000

出　　处：《中国海洋大学学报（自然科学版）》2020年第8期19-24,共6页Periodical of Ocean University of China

基　　金：国家自然科学基金重点项目(91958206);中央高校基本科研业务费项目(201813024)资助。

摘　　要：本文讨论了变系数KdV方程的一种求解方法及其理论应用。首先利用解析解给出初值条件,其次通过龙格库塔法结合显格式差分法对方程进行离散,并运用MATLAB软件编程求出方程的数值解。为了更好地体现孤立波的特性,本文选取了不同的初始波形,以研究孤立波的极性转换、线性化及频散产生尾波等典型情形,并将此理论用于实际海洋的孤立波分析中,以便更简洁直观地了解内孤立波的特性。This paper mainly discusses a solution method and its theoretical application of the variable coefficient KdV equation.Firstly,the initial value condition is given by the analytical solution,and then the equation is discretized by the Runge-Kutta method combined with the explicit format difference method,and the MATLAB software is used to calculate the numerical solution of the equation.In order to reflect the characteristics of solitary waves better,this paper selects different initial waveforms,studies the typical cases of polar wave transform-ation,linearization and dispersion to generate wake waves,and applies this theory to the solitary wave of actual oceans in order to understand the characteristics of the inner solitary wave more concisely and intuitively.

关 键 词：龙格库塔法 变系数KDV方程 极性转化 上凸型内孤立波 

分 类 号：O242.1[理学—计算数学]