Analytical investigation of focusing Bose-Einstein condensates

The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use scaling solution method comprising time-dependent function to analytically examine the dynamics falling in different regimes propagation including expansion and compression zones. Our model based on Gross--Pitaevskii equation which involves interparticle interactions between atoms and, consequently, their influence focused structures. investigate profile characteristic factors such as resolution peak density for various cases optical potential parameters well associated with moving cloud. results are compared numerical solutions equation.