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In this work, we have studied a traveling wave packet when it travels through a rectangular quantum barrier and well. For this purpose, we have calculated the reflection, trapping and transmission coefficient of the cited quantum systems. We show that trapped part of the wave packet increases and then decreases with time. Deeper quantum wells have smaller trapping coefficient while higher quantum barriers have larger trapping coefficient. Changing of the velocity of the wave packet does not change the trapping coefficient. For small barrier heights (well depths), the reflection increases and then approximately saturates when the nonlinear coefficient increases. Finally, there are abrupt changes in the reflection, trapping and transmission coefficients when the barrier (or well) widths increase.

In this work, we have studied a traveling soliton through a triangular refractive index waveguide. Our calculations have been performed with a 4th order Runge Kutta method which we have presented the algorithm. Then we have checked the numerical accuracy and found it desirable. In our investigations, the light beam inside a waveguide have been oscillated which perfectly agree with the so-called “swing effect”. In comparison with a soliton with amplitude Q = 1, for soliton amplitude Q = 2 a shorter oscillation period have been observed. In the meantime, for lower waveguide widths, soliton have had shorter oscillation period. Finally, for η ≠ 0, the soliton oscillate with higher amplitude and it recede from center of waveguide which is not desirable.