Topological and non-topological soliton solutions to the 1 + 3-dimensional Gross-Pitaevskii equation with quadratic potential term

This paper carries out the integration of the 1 + 3-dimensional Gross- Pitaevskii Equation (GPE) in presence of quadratic potential term to obtain the 1-soliton solutions. The solitary wave ansatz method is employed to integrate the considered equation. Parametric conditions for the existence of the soliton solutions are determined. Both non-topological (bright) and topological (dark) soliton solutions are reported and we observed that the existence condition for bright and dark soliton solutions were opposite to each other. Finally, the two integrals of motion of the governing model equation have been extracted.