On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: a soliton doublet

TL;DR

This paper investigates a Boussinesq-type wave equation with displacement-dependent nonlinearity, revealing the existence of a novel soliton doublet through phase plane analysis and numerical simulations, with applications to biomembrane wave dynamics.

Contribution

It introduces a new solution type, the soliton doublet, for a Boussinesq-type equation with displacement-dependent nonlinearities, supported by analytical and numerical methods.

Findings

Existence of soliton doublets demonstrated

Phase plane analysis confirms solution stability

Numerical simulations support theoretical predictions

Abstract

In this paper the permanent profile waves governed by a Boussinesq-type wave equation are analysed. The model involves displacement-type nonlinearities and dispersion terms. Physically such a model equation describes longitudinal waves (density change) in biomembranes which have an internal structure composed by lipid molecules. The possible solutions are constructed and analysed. The phase plane analysis and numerical simulation reveal a novel phenomenon: the possible existence of a soliton doublet.