摘要
Based on the fundamental commutator representation proposed by Cao [4] we established two explicit expressions for roots of a third order differential operator. By using those expressions we succeeded in clarifying the relationship between two major approaches in theory of integrable systems： the zero curvature and the Lax representations for the KdV and the Boussinesq hierarchies. The proposed procedure could be extended to the general case of higher order of differential operators that leads to the Gel＇fand-Dickey hierarchy.
Based on the fundamental commutator representation proposed by Cao [4] we established two explicit expressions for roots of a third order differential operator. By using those expressions we succeeded in clarifying the relationship between two major approaches in theory of integrable systems： the zero curvature and the Lax representations for the KdV and the Boussinesq hierarchies. The proposed procedure could be extended to the general case of higher order of differential operators that leads to the Gel＇fand-Dickey hierarchy.
基金
Supported by the National Natural Science Foundation of China(No.11275129)
