Self-accelerating solitons

Abstract Basic models which give rise to one- and two-dimensional (1D 2D) solitons, such as the Gross-Pitaevskii (GP) equations for BEC, feature Galilean invariance, makes it possible generate families of moving solitons from quiescent ones. A challenging problem is find admitting stable self-accelerating (SA) motion solitons. SA modes are known in linear systems form Airy waves, but they poorly localized states. This brief review presents two-component BEC make predict In one system, a pair interacting 1D with opposite signs effective mass created binary trapped an optical-lattice potential. that case, interaction forces, acting on positive negative masses, produce equal accelerations, while total momentum conserved. The second model based system GP two atomic components, resonantly coupled by microwave field. latter produces exact transformation accelerating references frame, thus predicting 2D including vortex rings.