  In this paper, to study the effects of a nonlinear medium on the atom-field
interaction, we use the nonlinear coherent states approach. For this purpose,
we choose the two-mode cross-Kerr as the our nonlinear optical phenomena and
with the use of it's algebra, we show that it can be described equivalently by
a deformed oscillator algebra and also, by a deformed (su(2)) algebra. Then, we
construct the associated coherent states and investigate their statistical
properties. After that, as an example of applicability of the constructed
two-mode nonlinear coherent states, we investigate the nonlinear effects of the
medium on the dynamics of atom-field interaction within the framework of the
coherent states. By using the time-dependent Schr\"odinger equation, we first
obtain the atom-field state and then study the effect of the nonlinear medium
on the occupation probabilities of the atomic levels. In the following, we
consider the relation between the revival time of the atomic occupation
probabilities and the nonlinear parameter of the medium. Then, to study the
nonlinear effects on the dynamical properties of the cavity field, we consider
photon distribution, correlation function, Mandel parameters of the field, the
von Neumann entropy and the squeezing. Particularly, the nonlinearity of the
media on the nonclassical properties of two modes is clarified.
