正则化长波方程孤立波的数值模拟

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．

The Numerical Simulation of Solitary Wave on Regular Longwave Equation

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.