Extensions on two-component BKP and D type Drinfeld–Sokolov hierarchies

Abstract

In this article, we define a two-component coupled BKP hierarchy defined by four pseudo-differential Lax operators and construct its additional symmetries. These additional symmetries have a structure of a coupled $$w^B_{\infty }\times w^B_{\infty } $$ Lie algebra. Further we construct a new coupled D type Drinfeld–Sokolov hierarchy, which is a reduction of the two-component coupled BKP hierarchy, and the hierarchy possesses a complete Virasoro symmetry.