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

@article{Wu2010RmatricesAH,
  title={\$R\$-matrices and Hamiltonian Structures for Certain Lax Equations},
  author={Chao-Zhong Wu},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2010}
}
  • Chao-Zhong Wu
  • Published 23 December 2010
  • Mathematics
  • arXiv: Exactly Solvable and Integrable Systems
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. 

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