$R$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 biHamiltonian structures for each of the twocomponent BKP and the Toda lattice hierarchies. We also show that, when such two hierarchies are reduced to their subhierarchies, these biHamiltonian structures are reduced correspondingly.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 arXiv:
 arXiv:1012.5245
 Bibcode:
 2010arXiv1012.5245W
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 Rev. Math. Phys. 25, No. 3 (2013) 1350005, 27 pp