$R$-matrices and Hamiltonian Structures for Certain Lax Equations

Abstract

In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We also show that, when such two hierarchies are reduced to their subhierarchies, these bi-Hamiltonian structures are reduced correspondingly.

References in corpus (2)

• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

Cited by in corpus (1)

• From Additional Symmetries to Linearization of Virasoro Symmetries