Search for an Analytical Solution in the Three-Dimensional Gross–Pitaevskii Equation

Abstract

The Gross–Pitaevskii equation is at the core of the mathematical problem of the propagation of a Bose–Einstein condensate (BEC). In this article, we look for an analytical soliton solution in the three-dimensional Gross–Pitaevskii equation. We compare our analytical solution with the various numerical soliton solutions (dark solitons, light solitons, reflected solitons) reported by many researchers for the case of BEC interacting with an external potential (an obstacle, a magnetic trap, etc.). Our analytical solution can be applied to find both the main and the reflected soliton solution.