  A unifying scheme based on an ancestor model is proposed for generating a
wide range of integrable discrete and continuum as well as inhomogeneous and
hybrid models. They include in particular discrete versions of sine-Gordon,
Landau-Lifshitz, nonlinear Schr\"odinger (NLS), derivative NLS equations,
Liouville model, (non-)relativistic Toda chain, Ablowitz-Ladik model etc. Our
scheme introduces the possibility of building a novel class of integrable
hybrid systems including multi-component models like massive Thirring, discrete
self trapping, two-mode derivative NLS by combining different descendant
models. We also construct inhomogeneous systems like Gaudin model including new
ones like variable mass sine-Gordon, variable coefficient NLS, Ablowitz-Ladik,
Toda chains etc. keeping their flows isospectral, as opposed to the standard
approach. All our models are generated from the same ancestor Lax operator (or
its q -> 1 limit) and satisfy the classical Yang-Baxter equation sharing the
same r-matrix. This reveals an inherent universality in these diverse systems,
which become explicit at their action-angle level.
