On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: a soliton doublet
Pattern Formation and Solitons
2018-11-14 v1 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1806.10334,
title = {On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: a soliton doublet},
author = {Tanel Peets and Kert Tamm and Päivo Simson and Jüri Engelbrecht},
journal= {arXiv preprint arXiv:1806.10334},
year = {2018}
}