We investigate the solutions of a one-dimensional mean-field hydrodynamic equation using a variational approximation (VA). We analytically model and compare two Bose-Einstein condensates which can be used to create bright gap solitons experimentally, one of them trapped by a double-periodic optical lattice and the other one trapped by a single-periodic optical lattice. No additional harmonic confinement was employed in both cases. Through the variational approximation, we study the possibility that the nonlinearity coefficient, in a combination with the potential of either the double-periodic or the single-periodic optical lattice, allows the appearance of one dimensional bright gap solitons. In both cases, we analyze the existence and stability of bright gap solitons using a Gaussian ansatz. This paper can be used as a learning guide in the study of cold atoms. Students are encouraged to perform variational calculations for other types of optical lattices.
Bose-Einstein condensate; optical lattices; variational approximation; bright gap solitons
