  We demonstrate that superpositions of coherent and displaced Fock states,
also referred to as generalized Schr\"odinger cats cats, can be created by
application of a nonlinear displacement operator which is a deformed version of
the Glauber displacement operator. Consequently, such generalized cat states
can be formally considered as nonlinear coherent states. We then show that
Glauber-Fock photonic lattices endowed with alternating positive and negative
coupling coefficients give rise to classical analogs of such cat states. In
addition, it is pointed out that the analytic propagator of these deformed
Glauber-Fock arrays explicitly contains the Wigner operator opening the
possibility to observe Wigner functions of the quantum harmonic oscillator in
the classical domain.
