We investigate the solution of a mean-field-hydrodynamic equation using variational approximation with the aim of study the formation of fundamental gap solitons in a Bose gas and in a degenerate Fermi gas when trapped by one transversal potential and a single-periodic one-dimensional optical lattice. By variational approximation we study the possibility that the effective nonlinearity or interaction coefficient acting in combination with the potential of the optical lattice which allows the appearance of solitons in different dimensions presenting a peculiar behavior in function of the chemical potential.
Bose-Einstein condensate; degenerate Fermi gas; variational approximation (VA)
