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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (6): 646-654.doi: 10.3969/j.issn.1005-3085.2017.06.008

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Ito型耦合KdV方程的高阶保能量方法

王一帆,   孙建强,   陈宵玮   

  1. 海南大学信息科学技术学院，海口  570228
  • 收稿日期:2016-06-22 接受日期:2016-11-30 出版日期:2017-12-15 发布日期:2018-02-15
  • 基金资助:
    国家自然科学基金(11561018)；海南省自然科学基金(20167246).

High Order Energy Preserving Method for the Ito-type Coupled KdV Equations

WANG Yi-fan,   SUN Jian-qiang,   CHEN Xiao-wei   

  1. College of Information Science and Technology, Hainan University, Haikou 570228
  • Received:2016-06-22 Accepted:2016-11-30 Online:2017-12-15 Published:2018-02-15
  • Supported by:
    The National Natural Science Foundation of China (11561018); the Natural Science Foundation of Hainan Province (20167246).

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摘要： 构造具有能量守恒特性的Ito型耦合KdV方程的高阶保能量格式在模拟方程的运动中有重要的意义．本文利用四阶平均向量场方法和拟谱方法得到了Ito型耦合KdV方程的高阶保能量格式，并利用高阶保能量格式数值模拟方程孤立波的演化行为．数值结果表明新的高阶保能量格式能很好地模拟Ito型耦合KdV方程孤立波的行为，且精确地保持了方程的离散能量守恒．

关键词: 平均向量场方法, 高阶保能量方法, 孤立波, Ito型耦合KdV方程

Abstract: Constructing the high order energy preserving scheme for the Ito-type coupled KdV equation with the energy conservation property has the important application in simulating the motion of the equation. In this paper, the high order energy preserving scheme for the Ito-type coupled KdV equation is obtained by applying the fourth order average vector field method and the Fourier pseudo spectral method. The new high order energy preserving scheme is applied to simulate the solitary wave behaviors  of the equation. Numerical results show the new high order energy preserving scheme can well simulate the solitary wave evolution behaviors of the Ito-type coupled KdV equation and preserve the discrete energy conservation exactly.

Key words: average vector field method, high order energy-preserving method, the solitary wave, the Ito-type coupled KdV equation

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