一个新的非线性演化方程族及其拟哈密顿结构（英文）  

New nonlinear evolution equation hierarchy and their quasi-Hamiltonian structures

作　　者：金秋艳 李倩 夏铁成[1] JIN Qiuyan;LI Qian;XIA Tiecheng(College of Sciences,Shanghai University,Shanghai 200444,China;College of Sciences,Zhengzhou Institute of Aeronautical Industry Management,Zhengzhou 450005,China)

机构地区：[1]上海大学理学院,上海200444 [2]郑州航空工业管理学院理学院,郑州450005

出　　处：《应用数学与计算数学学报》2018年第3期686-696,共11页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Foundation of China(11271008,61640315);the First-Class Discipline of University in Shanghai and the Shanghai University Leading Academic Discipline Project(A.13-0101-12-004)

摘　　要：从3×3谱问题出发,提出了一种新的非平凡的非线性演化方程族.在迹恒等式的帮助下,构造拟哈密顿结构.其次,讨论了它的刘维尔可积性.最后,基于线性谱问题,得到了该方程族无穷多守恒律中前两个成员的守恒定律.Starting from the 3×3 matrix spectral problem,a novel nonlinear evolution equation hierarchy is proposed.With the help of the trace identity,the quasi-Hamiltonian structures of the hierarchy are constructed.Furthermore,we discuss its Liouville integrability.Finally,the infinite many conservation laws of the first two members in the hierarchy are obtained based on two linear spectral problems.

关 键 词：刘维尔可积 拟哈密顿结构 守恒律 

分 类 号：O175.14[理学—数学]