正则化长波方程孤立波的数值模拟  

The Numerical Simulation of Solitary Wave on Regular Longwave Equation

作　　者：王巧龙[1] 黄明游[2] 

机构地区：[1]中国人民解放军农牧大学基础部,长春130062 [2]吉林大学数学研究所,长春130023

出　　处：《吉林大学自然科学学报》1997年第3期1-13,共13页Acta Scientiarum Naturalium Universitatis Jilinensis

摘　　要：构造了求解正则化长波方程的一种Fourier－Galerkin－CenterEuler全离散格式，该格式具有质量与能量守恒性质和保持原微分方程结构等优点．证明了半离散和全离散格式解的存在唯一性，并得到误差估计式．此外，给出了两个数值例子，使用文中提出的全离散格式成功地模拟了单孤立波的传播和双孤立波的碰撞过程．This paper gives a kind of Fourier-Galerkin-Center Euler fully discrete scheme for the numerical computation of regular longwave equation, which has advanteges such as conservation properties of mass and energy, preserving structure of the original differential equation, etc. It proves that there exists the unique solution both for the semidiscrete scheme and the fully discrete scheme, and some error estimates of the approximate solution are obtained. In addition, the paper gives two numerical examples, the propogation of single soliton and the collision process of two solitons are simulated by making use of the fully discrete scheme proposed in the paper.

关 键 词：正则化长波方程 孤立波 数值模拟 守恒格式 

分 类 号：O241.82[理学—计算数学]