In an effort to meet an ever increasing demand for more accurate and realistic integrated photonics simulations, we have developed a multidimensional, nonlinear finite difference time domain (NL-FDTD) Maxwell's equations solver. The NL-FDTD approach and its application to the modeling of the interaction of an ultrashort, optical pulsed Gaussian beam with a Kerr nonlinear material will be described. Typical examples from our studies of pulsed-beam self-focusng, the scattering of a pulsed-beam from a linear-nonlinear interface, and pulsed-beam propagation in nonlinear waveguides will be discussed.