A Few Integrable Couplings of Some Integrable Systems and ( 2 + 1 )-Dimensional Integrable Hierarchies

Abstract

Two high-dimensional Lie algebras are presented for which four ($1+1$)-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the AKNS hierarchy. Then ($2+1$)-dimensional DS hierarchy is derived by using the TAH scheme; in particular, the integrable couplings of the DS hierarchy are obtained.