Structure preserving algorithms for soliton equations

The structure preserving 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.