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.

中文翻译：

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两部分BKP和D型Drinfeld–Sokolov层次结构的扩展

在本文中，我们定义了由四个伪微分Lax运算符定义的两成分耦合BKP层次结构，并构造了其其他对称性。这些附加的对称性具有耦合\（w ^ B _ {\ infty} \乘以w ^ B _ {\ infty} \）李代数的结构。进一步，我们构造了一个新的耦合D型Drinfeld-Sokolov层次结构，它是两成分耦合BKP层次结构的简化，并且该层次结构具有完整的Virasoro对称性。