Domain walls of single-component Bose-Einstein condensates in external potentials

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 magnetic trap can stabilize it. Stable solutions also include “twisted” domain walls, as well as asymmetric solitons. The results apply as well to spatial solitons in planar nonlinear optical waveguides with transverse modulation of the refractive index.