  In this paper the theory and simulation results are presented for 3D
cylindrical rotationally symmetric spatial soliton propagation in a nonlinear
medium using a modified finite-difference time-domain general vector auxiliary
differential equation method for transverse magnetic polarization. The theory
of 3D rotationally symmetric spatial solitons is discussed, and compared with
two (1+1)D, termed "2D" for this paper, hyperbolic secant spatial solitons,
with a phase difference of pi (antiphase). The simulated behavior of the 3D
rotationally symmetric soliton was compared with the interaction of the two
antiphase 2D solitons for different source hyperbolic secant separation
distances. Lastly, we offer some possible explanations for the simulated
soliton behavior.
