摘要
本文讨论变形KdV方程的解法。首先借助B(?)cklund变换的不变性定理和置换定理导出该方程孤立波传播及孤立子相互作用的分析解,然后用Petrov-Galerkin有限元法建立了求数值解的格式并以分析解提供的初值,数值地求解了该方程的Cauchy初值问题。所得数值解与分析解的高度吻合既印证了理论方法的正确性,也显示了数值方法的高精度和稳定性。
This Paper deals with the initial value problems of the Modified KdV(MKdV) equation. First, the analytic solutions of solitary wave and interaction of two solitons are obtained by the Backlund Transformation. Then, a numerical scheme of a kind of Petrov-Galerkin finite element methods is derived and used to solve the initial value problems of MKdV equation numerically. Finally, the comparison of numerical and analytic solutions is made and shows the excellent accurancy and stability of the numerical scheme used in this paper.
出处
《计算物理》
CSCD
北大核心
1989年第4期399-406,共8页
Chinese Journal of Computational Physics
