Multi-component hierarchies of double bracket equations.
The aim of the present paper is to extend previous results to the matrix case. By using a matrix first-order pseudo-differential Lax operator, still more integrable gradient flows are presented. These equations are united by a hierachy called the matrix Brockett hierarchy. A new version of the Zakharov-Shabat-type equations is proved. Formal solutions of this hiearchy are constructed using a matrix double bracket bilinear identity.
scientific article; zbMATH DE number 2084222
scientific article