摘要
本文给出了一个2×2谱问题及其相应的孤子族,并利用此孤子族的Lenard算子对的性质,证明了该系统是具有Bi-Hamilton结构和Multi-Hamilton结构的广义Hamilton系统,进一步给出其Liouville可积性的证明.此外,值得提出的是此系统可约化为广义TD族、TD族和广义C-KdV族、C-KdV族等,并得到了该孤子族的Hamilton泛函与守恒密度之问的一一对应关系.
Based on a 2× 2 spectral problem, the corresponding hierarchy of evolution equations is derived. According to the property of its 2 × 2 Lenard pair of operators, it can be checked that the hierarchy is a generalized Hamilton system and possesses Bi-Hamilton structure and Multi-Hamilton structure. Furthermore, its Liouville inte- grability is also evidenced. What's more, this hierarchy, in special cases, can reduce to the general TD hierarchy, TD hierarchy, general C-KdV hierarchy, C-KdV hierarchy, etc. In the end, the one to one relation between the Hamilton functionals and the conservation densities are provided too.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2011年第1期15-22,共8页
Acta Mathematica Sinica:Chinese Series
基金
河南省基础与前沿技术研究计划项目(092300410187)
河南省教育厅自然科学基金研究项目(2009B110014
2008B110010)
洛阳师范学院青年自然科学基金项目(qnjj-2009-12)