Effect of interaction strength on gap solitons of Bose--Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose--Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose--Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose--Einstein condensate.