Spatial soliton propagation through a triangular waveguide: A Runge Kutta study

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.