Mechanisms of formation of gap solitons of Bose-Einstein condensates in optical lattices

It is known that solitons of Bose-Einstein condensates with positive scattering lengths can be produced in optical lattices. The key of this process is the negative sign of the effective mass of the wavepacket as it comes closer to the edge of the first Brillouin zone. However, the underlying assumption of the effective mass approach is the slow variation of the wavefunction envelope between consecutive lattice cells. Previous experiments and computations on this type of solitons show that this is not the usual case. In this contribution we will go beyond the slowly varying assumption to demonstrate that the equations governing the dynamics of gap solitons contain a third derivative in the dispersion. As a result, the dynamics of the stabilized wavepackets is found different that the soliton's. In particular, a radiative component is present, and the stability under collisions is only partially achieved.