Variational method to spatial soliton propagation in a waveguide with periodic parabolic index profile

In this paper, we study spatial soliton propagation in a waveguide with periodic parabolic refractive index profile. Wave equation in the present of the refractive index profile includes diffraction, self-focusing (SF) and self-defocusing (SDF). To solve the wave equation, we use variational method and finally discuss the effect of self-defocusing and maximum potential depth on soliton behaviour.