We demonstrate the possibility of creating domain walls described by a single component Gross–Pitaevskii equation with attractive interactions, in the presence of an optical–lattice potential. While it is found that the domain wall is unstable in an infinite system, we show that the external...

We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose–Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with...

We study the dynamics of solitons in Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC,...