3 years ago

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

Tanel Peets, Kert Tamm, Päivo Simson, Jüri Engelbrecht

Publication date: Available online 10 November 2018

Source: Wave Motion

Author(s): Tanel Peets, Kert Tamm, Päivo Simson, Jüri Engelbrecht


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.

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