# Interactions of solitons with positive and negative masses: Shuttle motion and co-acceleration

## TL;DR

This paper explores the dynamics of soliton pairs with positive and negative effective masses in a two-component BEC within an optical lattice, revealing regimes like shuttle oscillations, splitting, and co-acceleration, and demonstrating control via gravity potential.

## Contribution

It introduces a new understanding of self-accelerating soliton pairs with mixed masses in BECs, including regimes and control mechanisms, supported by simulations and variational approximation.

## Key findings

- Shuttle oscillations and splitting regimes identified.
- Co-acceleration occurs at the boundary between regimes.
- Gravity potential can control soliton dynamics.

## Abstract

We consider a possibility to realize self-accelerating motion of interacting states with effective positive and negative masses in the form of pairs of solitons in two-component BEC loaded in an optical-lattice (OL) potential. A crucial role is played by the fact that gap solitons may feature a negative dynamical mass, keeping their mobility in the OL. First, the respective system of coupled Gross-Pitaevskii equations (GPEs) is reduced to a system of equations for envelopes of the lattice wave functions. Two generic dynamical regimes are revealed by simulations of the reduced system, viz., shuttle oscillations of pairs of solitons with positive and negative masses, and splitting of the pair. The co-accelerating motion of the interacting solitons, which keeps constant separation between them, occurs at the boundary between the shuttle motion and splitting. The position of the co-acceleration regime in the system's parameter space can be adjusted with the help of an additional gravity potential, which induces its own acceleration, that may offset the relative acceleration of the two solitons, while gravity masses of both solitons remain positive. The numerical findings are accurately reproduced by a variational approximation. Collisions between shuttling or co-accelerating soliton pairs do not alter the character of the dynamical regime. Finally, regimes of the shuttle motion, co-acceleration, and splitting are corroborated by simulations of the original GPE system, with the explicitly present OL potential.