  A family of completely integrable nonlinear deformations of systems of N
harmonic oscillators are constructed from the non-standard quantum deformation
of the sl(2,R) algebra. Explicit expressions for all the associated integrals
of motion are given, and the long-range nature of the interactions introduced
by the deformation is shown to be linked to the underlying coalgebra structure.
Separability and superintegrability properties of such systems are analysed,
and their connection with classical angular momentum chains is used to
construct a non-standard integrable deformation of the XXX hyperbolic Gaudin
system.

Exactly Solvable and Integrable Systems;Quantum Algebra;Exactly Solvable and Integrable Systems