Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

The Homotopy Analysis Method (HAM) is adopted to find the approximate analytical solutions of the Gross-Pitaevskii equation, a nonlinear Schrödinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is weakly.