4×4B-型KdV方程族

4×4 B-Type KdV Hierarchies

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算子B统一得到.对所有可能的线性算子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cklund变换.

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 Backlund transformations by the loop group method.