Optical solitons of transmission equation of ultra-short optical pulse in parabolic law media with the aid of Backlund transformation

The Backlund transformation is used to obtain optical soliton for a type of the Schrödinger equation. Kink-type and dark-optical soliton solutions are acquired of the Schrödinger equation. It is illustrated that the examined equation is integrable because if an equation has a Backlund transformation it could be integrable. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions. The numerical simulations supplement the analytical schemes.