An algorithm and its application for obtaining  some kind of infinite-dimensional Hamiltonian canonical
formulation

doi:10.1088/1009-1963/16/11/002

中国物理B ›› 2007, Vol. 16 ›› Issue (11): 3154-3160.doi: 10.1088/1009-1963/16/11/002

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

阿拉坦仓¹, 任文秀²

(1)Department of Mathematics, Inner Mongolia University, Hohhot 010021, China; (2)Department of Mathematics, Inner Mongolia University, Hohhot 010021, China；Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China

收稿日期:2007-05-09 修回日期:2007-07-19 出版日期:2007-11-20 发布日期:2007-11-20
基金资助:
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).

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

Ren Wen-Xiu(任文秀)^{a) b)} and Alatancang(阿拉坦仓)^a)†

^a Department of Mathematics, Inner Mongolia University, Hohhot 010021, China; ^b Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China

Received:2007-05-09 Revised:2007-07-19 Online:2007-11-20 Published:2007-11-20
Supported by:
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).

摘要/Abstract

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 $`{\partial}/{\partial x}$'-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.

关键词: evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutator

Abstract: 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 ` $\partial/\partial x$'-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.

Key words: nonlinear evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutator

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.30.Jr (Partial differential equations) 02.30.Tb (Operator theory) 02.30.Zz (Inverse problems)

任文秀, 阿拉坦仓. An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation[J]. 中国物理B, 2007, 16(11): 3154-3160.

Ren Wen-Xiu(任文秀) and Alatancang(阿拉坦仓). An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation[J]. Chinese Physics, 2007, 16(11): 3154-3160.

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An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

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