  We theoretically study the optical tomography of the time evolved states
generated by the evolution of different kinds of initial wave packets in a Kerr
medium. Exact analytical expression for the optical tomogram of the quantum
state at any instant during the evolution of a generic initial wave packet is
derived in terms of Hermite polynomials. Time evolution of the optical tomogram
is discussed for three kinds of initial states: a coherent state, an
$m$-photon-added coherent state, and even and odd coherent states. We show the
manifestation of revival and fractional revivals in the optical tomograms of
the time evolved states. We find that the optical tomogram of the time evolved
state at the instants of fractional revivals shows structures with sinusoidal
strands. The number of sinusoidal strands in the optical tomogram of the time
evolved state at $l$-sub-packet fractional revivals is $l$ times the number of
sinusoidal strands present in the optical tomogram of the initial state. We
have also investigated the effect of decoherence on the optical tomograms of
the states at the instants of fractional revivals for the initial states
considered above. We consider amplitude decay and phase damping models of
decoherence, and show the direct manifestations of decoherence in the optical
tomogram.
