Generation of soliton bubbles in a sine-Gordon system with localised inhomogeneities

TL;DR

This paper investigates how sine-Gordon solitons interact with localized inhomogeneities, leading to the formation of bubble-like structures influenced by internal modes and array configurations, with implications for physical and biological systems.

Contribution

It introduces a one-dimensional theory explaining the activation of internal modes and formation of bubble structures during soliton-inhomogeneity interactions, highlighting the role of inhomogeneity arrays.

Findings

Internal modes can be activated depending on inhomogeneity topology

Shape mode instabilities lead to bubble and drop structures

Structures are stabilized by arrays of localized inhomogeneities

Abstract

Nonlinear wave propagation plays a crucial role in the functioning of many physical and biophysical systems. In the propagation regime, disturbances due to the presence of local external perturbations, such as localised defects or boundary interphase walls have gained great attention. In this article, the complex phenomena that occur when sine-Gordon line solitons collide with localised inhomogeneities are investigated. By a one-dimensional theory, it is shown that internal modes of two-dimensional sine-Gordon solitons can be activated depending on the topological properties of the inhomogeneities. Shape mode instabilities cause the formation of bubble-like and drop-like structures for both stationary and travelling line solitons. It is shown that such structures are formed and stabilised by arrays of localised inhomogeneities distributed in space. Implications of the observed phenomena in physical and biological systems are discussed.