Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one-dimensional Bose–Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.