| 梅建琴.4×4B-型KdV方程族[J].数学年刊A辑,2012,33(2):161~174 |
| 4×4B-型KdV方程族 |
| 4×4 B-Type KdV Hierarchies |
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| DOI： |
| 中文关键词: 李代数分裂 B-型KdV方程族 Hamilton结构 B(a)cklund变换 |
| 英文关键词:Lie algebra splitting, B-type KdV hierarchy, Hamiltonian structure,
B¨acklund transformation |
| 基金项目:中央高校基本科研基金，国家留学基金资助的项目 |
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| 中文摘要: |
| 基于sl(4,(C))的loop代数的非平凡李代数分裂,构造了5类新的孤子方程族.这些代数分裂通过构造从正李子代数到负李子代数的线性箅子B统一得到.对所有可能的线性箅子B进行分类,证明存在5类4×4仿射B-型KdV方程族.利用Adler- Konstant- Symes理论获得了这些方程族的Hamilton结构,并利用loop群方法得到其B(a)cklund变换. |
| 英文摘要: |
| Based on nontrival splittings of the sl(4,C) loop algebra, five families of new
soliton hierarchies are constructed. These splittings come from a uniform method of constructing
splittings by a linear operator B from the positive Lie subalgebra to the negative
Lie subalgebra. The author classifies all the possibilities of the linear operator B and shows
that there are five families of 4×4 B-type KdV hierarchies. And the author gives the Hamiltonian
structures of these hierarchies via the Adler-Konstant-Symes theory and constructs
the B¨acklund transformations by the loop group method. |
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