# Nonlinear management of topological solitons in a spin-orbit-coupled system

## TL;DR

This paper explores how periodic modulation of cross-attraction strength in a spin-orbit-coupled system can control the stability and dynamics of topological solitons, revealing bistability regions and resonance-induced instabilities.

## Contribution

It introduces a method to manage soliton stability via time-periodic modulation of inter-component attraction in a spin-orbit-coupled system, uncovering new stability phenomena.

## Key findings

- Bistability regions for solitons near the critical gamma=1
- Emergence of stability tongues and instability troughs due to modulation
- Resonance effects between modulation and soliton modes

## Abstract

We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making the relative strength of the cross-attraction, gamma, a function of time periodically oscillating around the critical value, gamma = 1, which is an SD/MM stability boundary in the static system. The structure of SDs is represented by the combination of a fundamental soliton in one component and localized dipole mode in the other, while MMs combine fundamental and dipole terms in each component. Systematic numerical analysis reveals a finite bistability region for the SDs and MMs around gamma = 1, which does not exist in the absence of the periodic temporal modulation ("management"), as well as emergence of specific instability troughs and stability tongues for the solitons of both types, which may be explained as manifestations of resonances between the time-periodic modulation and intrinsic modes of the solitons. The system can be implemented in Bose-Einstein condensates, and emulated in nonlinear optical waveguides.