Bright and dark spatial solitons in coupled photorefractive media

We consider beam propagation in photorefractive media, where the pulse dynamics is governed by a set of coupled nonlinear Schrödinger-type equations. We construct anharmonic oscillator equations using the Stokes parameters and find a solution for bright spatial solitons in photorefractive media. We then reduce the anharmonic oscillator to the well-known undamped and unforced Duffing oscillator equation. From this equation, we present the necessary conditions for the formation of both bright and dark screening solitons, and obtain solutions for both of them