Wigner Functions of Time-Dependent Cat-Like Even/Odd Superpositions of Nonlinear Coherent States

We calculate and plot the Wigner functions of several families of highly excited even and odd superpositions of nonlinear coherent states, looking for conditions under which such superpositions can be interpreted as models of the ``Schr\"odinger cat'' states. It appears that the decisive factor is the form of the number distribution functions over the Fock basis: they must have well localized peaks. Otherwise, no ``cat'' structures are observed.