# Tail-free self-accelerating solitons and vortices

## TL;DR

This paper demonstrates the existence of robust, tailless self-accelerating solitons and vortices in two-component Bose-Einstein condensates influenced by long-range microwave-mediated interactions, with potential applications in optical media.

## Contribution

It introduces a novel mechanism for self-accelerating tailless solitons and vortices in BECs with long-range interactions, including effects of spin-orbit coupling and nonlinearities.

## Key findings

- Existence of 1D and 2D self-accelerating tailless solitons and vortices.
- Self-accelerating solitons can follow curved trajectories.
- Mechanism applicable to optical media with thermal nonlinearity.

## Abstract

Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.