A generalized cubic Volterra lattice hierarchy and its integrable couplings system

摘要

In terms of properties of the known loop algebra (A) over tilde (1) and difference operators, a new algebraic system chi is constructed. By using the algebraic system chi, a discrete matrix spectral problem is introduced and a hierarchy of nonlinear lattice equations is derived. From the hierarchy the celebrated cubic Volterra lattice equation is engendered. We call the hierarchy a generalized cubic Volterra hierarchy. Then an extended algebraic system (chi) over tilde of chi is presented, from which the integrable couplings system of the generalized cubic Volterra lattice are obtained. (c) 2005 Elsevier Ltd. All rights reserved.