Exact soliton solutions of Gross Pitaevskii equation with a variable shape optical lattice potential

We study the existence of localized matter waves in Bose Einstein condensate (BEC) loaded into variable shape optical lattice (OL) potential. Similarity transformation is used to solve Gross-Pitaevskii equation (GPE) with space and time dependent coefficients. Bright and dark soliton solutions are obtained depending on the nonlinearities being focusing or defocusing. We analyze how the parameters of OL affect the properties of the soliton solutions. We also employ direct numerical simulations to prove the stability of the solutions and determine the parameter region in which the solutions are stable.