关键词: 孤立波方程, 保结构算法, 复合方法, 局部守恒格式, 数值实验

Abstract: The structure preservind difference algorithms for soliton equations are investigated. The symplectic structures and multisymplectic structures of the classical solitary wave equations such as the KdV, sine-Gordon and KP equations are presented to illustrate the applicability of the symplectic and multisymplectic algorithms. The concept of local conservative schemes and generalized structure preserving algorithms, which are natural generalizations of the structure preserving algorithms, are also proposed. A new concatenating method to systematically construct local conservative schemes and some numerical experiments of the constructed schemes are also presented.

Key words: soliton equations, structure preserving algorithms, concatenating method, local conservative schemes, numerical experiments