# The Affective Factors on the Uncertainty in the Collisions of the Soliton Solutions of the Double Field sine-Gordon System

## TL;DR

This paper investigates how affective factors influence the uncertainty during collisions of soliton solutions in a symmetric coupled sine-Gordon system, revealing that amplitude and phase variations affect collision outcomes.

## Contribution

It introduces a coupled sine-Gordon model with multiple soliton solutions and analyzes how localized wave packets impact collision uncertainties through numerical simulations.

## Key findings

- Collision uncertainty depends on wave packet amplitude
- Initial phase differences influence soliton collision outcomes
- Multiple topological solitons exhibit distinct interaction behaviors

## Abstract

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will be shown numerically, during collisions between solitons, there will be an uncertainty which originates from the amount of the maximum amplitude and arbitrary initial phases of the trapped wave packets.