一族新的离散可积双哈密顿系统  

A novel family of discrete bi-Hamiltonian systems

作　　者：吴迪[1] 

机构地区：[1]山东科技大学数学系

出　　处：《科技视界》2017年第6期166-168,共3页Science & Technology Vision

摘　　要：数年来,科学界对孤立子的研究呈不断发展进步趋势,许多领域中都存在孤立子现象以及与孤立子密切相关的问题,比如,在对无中心Virasoro对称代数或孤立子方程进行研究时产生的可积耦合系统。目前,学术界已找到多种求解可积耦合的方法:1,摄动;2,拓展相应的Lax对;3,拓展新的Loop代数;4,运用半直和李代数。首先通过离散零曲率方程得到一族新的可积晶格方程,再由迹-恒等式建立一个双-哈密顿结构,最后,证明了该方程族是Liouville可积的。Soliton theory research is developing in many scientific fields and there exists soliton and soliton theory closely related problems, integrable coupling system is in the center of the study without Virasoro algebra or symmetrically soliton equation. Scientists have found many integrable coupling methods： one, the perturbation method; two, expand the corresponding method of Lax on; three, extend new Loop algebra of the method; four, the use of a half straight and lie algebra method. A novel family of integrable lattice equation is derived from the discrete zero curvature equations. A bi-Hamiltonian structure of obtained family is established by discrete trace identity. Then, Liouville integrability for the obtained family is demonstrated.

关 键 词：可积晶格方程 双-哈密顿结构 LIOUVILLE可积 

分 类 号：O411.1[理学—理论物理]