Stability of coupled solitary wave in biomembranes and nerves

TL;DR

This study investigates the stability of coupled solitary waves in biomembranes and nerves, revealing how damping and inertia influence wave stability and profiles through a variational approach.

Contribution

It introduces a variational method to analyze coupled nonlinear wave stability in biomembranes, considering damping effects within the BKdV-BBM framework.

Findings

Inertia enhances wave stability.

Damping reduces stability and creates stable island regions.

Bell-shaped waves are stable; shock-like waves are unstable.

Abstract

In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using, the variational approach, the characteristics of the coupled solitary waves in the presence of damping within the framework of coupled nonlinear Burger-Korteweg-de Vries-Benjamin-Bona-Mahony (BKdV-BBM) equation. It is shown that, the inertia parameter increases the stability of coupled solitary waves while the damping parameter decreases it. Moreover, the presence of damping term induces a discontinuity of stable regions in the inertia-speed parameter space, appearing in he form of an island of points. Bell shape and solitary-shock like wave profiles were obtained by varying the propagation speed and their linear stability spectrum computed. It is shown that bell shape solitary wave exhibit bound state eigenvalue spectrum, therefore stable. On the other hand, the solitary-shock like wave profiles exhibit unbound state eigenvalue spectrum and are therefore generally unstable.