Matter-wave bright solitons: Internal atomic recombination and external feeding

We consider matter-wave bright solitons in the presence of three-body atomic recombination, an axial periodic modulation and a feeding term, and use a variational method to derive conditions to have dynamically stabilized solitons due to compensation between the dissipation and alimentation of atoms from external sources. We critically examine how the BEC soliton is affected by the imbalance between the internal atom loss and external feeding. We pay special attention to study the influence of these terms on the soliton dynamics in optical lattice potentials that cause periodic modulation.