Search for Soliton Solutions in the Three-Dimensional Gross–Pitaevskii Equation

Abstract

The article proposes an iterative method to find soliton solutions of the three-dimensional Gross---Pitaevskii equation that describes the interaction of a Bose---Einstein condensate with an external potential (a magnetic trap, an obstacle, etc.). The method finds both primary and reflected soliton solutions. It can also be applied to find soliton solutions of other nonlinear differential evolution equations. The method can be efficiently implemented on parallel computer systems, producing high-accuracy soliton solutions.