# Dynamics of the multi-soliton waves in the sine-Gordon model with two identical point impurities

## TL;DR

This paper investigates the behavior of multi-soliton waves in the sine-Gordon model with two point impurities, combining numerical simulations and analytical models to understand their dynamics and frequency dependence.

## Contribution

It introduces a combined numerical and analytical approach to study multi-soliton dynamics in a sine-Gordon model with impurities, highlighting the effects of impurity distance.

## Key findings

- Frequency dependence of localized waves on impurity distance
- Numerical investigation of quadrons structure and properties
- Analytical model using perturbation theory aligns with simulations

## Abstract

The particular type of four-kink multi-solitons (or quadrons) adiabatic dynamics of the sine-Gordon equation in a model with two identical point attracting impurities has been studied. This model can be used for describing magnetization localized waves in multilayer ferromagnet. The quadrons structure and properties has been numerically investigated. The cases of both large and small distances between impurities has been viewed. The dependence of the localized in impurity region nonlinear high-amplitude waves frequencies on the distance between the impurities has been found. For an analytical description of two bound localized on impurities nonlinear waves dynamics, using perturbation theory, the system of differential equations for harmonic oscillators with elastic link has been found. The analytical model qualitatively describes the results of the sine-Gordon equation numerical simulation.

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Source: https://tomesphere.com/paper/1702.06987