  The short range revival of an arbitrary monochromatic optical field, which
propagates in a quadratic GRIN rod, is a well-known effect that is established
assuming the first-order approximation of the propagation operator. We discuss
the revival and multiple splitting of an off-axis Gaussian beam propagating to
relatively long distances in a quadratic GRIN medium. These effects are
obtained assuming the second-order approximation of the propagation operator in
this medium.
