Self-accelerating solitons

Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University - Tel Aviv 69978, Israel and Instituto de Alta Investigación, Universidad de Tarapacá - Casilla 7D, Arica, Chile

^(a) E-mail: malomed@post.tau.ac.il (corresponding author)

Received: 8 August 2022
Accepted: 4 October 2022

Abstract

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