A symplectic realization of the Volterra lattice

TL;DR

This paper constructs a symplectic realization of the Volterra lattice, revealing its Hamiltonian structure, invariants, and symmetries through recursion operators, enhancing understanding of its integrability.

Contribution

It introduces a symplectic realization of the Volterra lattice and derives its hierarchy of invariants and brackets using recursion operators.

Findings

Hierarchy of invariants rediscovered

Poisson brackets characterized

Symplectic realization constructed

Abstract

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.