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.
Highlights
The propagation of nonlinear waves in inhomogeneous media has captured much recent interest in physics and biophysics [1]
Nonlinear pulse excitations regulate the functioning in many physical models of biological systems, such as the Purkinje’s fibres of the cardiac muscles [2, 3], neural fibres [4], DNA chains [5,6] and muscular networks [7]
A similar situation occurs in the propagation of topological one-dimensional solitons in DNA chains, which has been considered as a suitable model to explain the formation of open states or bubbles in the double helix [8]
Summary
The propagation of nonlinear waves in inhomogeneous media has captured much recent interest in physics and biophysics [1]. Solitons with an internal structure, such as sine-Gordon (sG) kinks and breathers, may produce many remarkable phenomena when colliding with localised inhomogeneities. The structure formation is understood using the one-dimensional theory of activation of internal modes in sG solitons.
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