Multiple hamiltonian structures and lax pairs for bogoyavlensky–volterra systems

Abstract

Results on the Volterra model which is associated to the simple Lie algebra of type A n are extended to the Bogoyavlensky–Volterra systems of type B n, C n and D n. In particular we find Lax pairs, Hamiltonian and Casimir functions and multi-Hamiltonian structures. Moreover, we investigate recursion operators, higher Poisson brackets and master symmetries. © 2003 Taylor & Francis Group, LLC.