A strip waveguide with a nonlinear substrate is investigated numerical
ly. Both stationary wave propagation and Gaussian beam excitation were
simulated. The Crank-Nicolson finite-difference scheme, combined with
the transparent boundary condition, which employs no adjustable param
eters, was used in the three dimensional calculations. The numerics su
pport the statement that the stationary three dimensional nonlinear gu
ided waves are stable on propagation for propagation constants corresp
onding to the ascending branches of the nonlinear dispersion curves. W
e found that in certain conditions, unstable nonlinear guided waves de
cay by emitting a spatial solitary wave into the nonlinear self-focusi
ng substrate. Similar effects occur in the case of end firing of Gauss
ian beams in the nonlinear strip waveguide.