与2×2谱问题相关的孤子族及其无限维Bi-Hamilton结构  

A Soliton Hierarchy Associated with a 2 × 2 Matrix Spectral Problem and Their Infinite-dimensional Bi-Hamiltonian Structure

作　　者：王涛[1] 杨帆[1] 

机构地区：[1]郑州科技学院基础部,河南郑州450064

出　　处：《华北水利水电学院学报》2013年第5期124-128,共5页North China Institute of Water Conservancy and Hydroelectric Power

摘　　要：立足于一个2×2谱问题获得了3×3Lenard算子对（K，J），并由此导出一类非平凡的（1＋1）维孤子方程组．为研究其结构，通过定义新的Lenard递推序列{Gj}得到了该等谱方程组的2×2Lenard算子对（K，J），进而证明了此孤子族具有Bi-Hamilton结构且在Liouville意义下可积．Based on a 2 × 2 spectral problem, a 3 × 3 Lenard pair of operators and a new （ l ＋ 1 ） dimensional soliton hierarchy are presented. In order to investigate the Hamihonian structures of this soliton hierarchy, a new Lenard gradient sequence Gi and its corresponding 2 × 2 Lenard pair of operators （ I（, j ） are introduced. Thus it is proved the soliton hierarchy possesses the Bi-Hamilton structures and Liouville integrability.

关 键 词：Lax可积孤子族 HAMILTON算子 Bi-Hamilton结构 LIOUVILLE可积 

分 类 号：O175.1[理学—数学]