摘要
Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.
Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.
基金
Project supported by the National Natural Science Foundation of China （Grant No 10562002） and the Natural Science Foundation of Nei Mongol, China （Grant No 200508010103）.
