NUMERICAL SIMULATIONS OF SOLITON PROPAGATION IN KERR NONLINEAR MEDIA WITH LINEAR REFRACTIVE INDEX VARIATION AND NONLINEAR DIFFRACTION

In this paper, a mathematical model is constructed by studying the effects of linear refractive index variations and nonlinear diffraction on soliton propagation. The complexity of the soliton model is further demonstrated through numerical simulations using the Crank-Nicolson scheme. The Crank-Nicolson is shown to be second order accurate in both the transversal and propagation directions. Our numerical simulations show that the linear refractive index triggers transverse oscillations, nonlinear diffraction causes energy leakage, and the combination of both results in shape changes and peak intensity shifts.