  In this work we examine a nonlinear version of the Jaynes-Cummings model for
two identical two-level atoms allowing for Ising-like and dipole-dipole
interplays between them. The model is said to be nonlinear in the sense that it
can incorporate both a general intensity-dependent interaction between the
atomic system and the cavity field and/or the presence of a nonlinear medium
inside the cavity. As an example, we consider a particular type of atom-field
coupling based upon the so-called Buck-Sukumar model and a lossless Kerr-like
cavity. We describe the possible effects of such features on the evolution of
some quantities of current interest, such as atomic excitation, purity,
concurrence, the entropy of the field and the evolution of the latter in phase
space.
