We construct a family of integrable deformations of the Bogoyavlenskij-Itoh
systems and construct a Lax operator with spectral parameter for it. Our
approach is based on the construction of a family of compatible Poisson
structures for the undeformed system, whose Casimirs are shown to yield a
generating function for the integrals in involution of the deformed systems. We
show how these deformations are related to the Veselov-Shabat systems.Comment: 23 pages, 14 reference
