Bright soliton solution of a Gross–Pitaevskii equation

We theoretically and numerically study the bright soliton solutions of a Gross–Pitaevskii equation governing one-dimensional (1D)(cigar-shaped) Bose–Einstein condensates (BEC) trapped in an optical lattice of 1D structure. The analytical expression of bright soliton is derived by using the variational approximation, which completely matches the numerical results with a range of potential’s parameters. Moreover, we determined the parameter domains for the persistence and non-persistence of bright soliton solutions.