Study of Localized Solutions of the Nonlinear Discrete Model for Dipolar BEC in an Optical Lattice by the Homoclinic Orbit Method

Abstract

Abstract. We use homoclinic orbits to find solutions of a dynamical system of the dipolar Bose Einstein Condensate (BEC) in a deep optical lattice. The equation of motion is transformed to a two-dimensional map and its homoclinic orbits are computed numerically. Each homoclinic orbit leads to a different solution. These different solutions lead to different types of solitons. We also analyse the stability of the solutions.