The presence of solitons in bose-einstein condensates can be studied using nonlinear partial differential equation called the gross-pitaevskii equation. An analytical technique using darboux transformation with the lax technique is attempted. The best possible numerical technique among the split-step fourier method, crank nicolson finite difference method and the split-step crank nicolson method was analysed based on the merits and demerits of each method. Finally after both an analytical and numerical analysis of the gross-pitaevskii equation, the ideal conditions for the formation of various types of solitons were identified.