2016/06/24 by Jüri Engelbrecht, Kert Tamm, Tanel Peets
Materials Science · Mathematics · Physics and Astronomy · #Korteweg–de Vries equation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Nonlocal and gradient elasticity in micro/nano structures #Periodic wave #Process (computing) #Range (aeronautics) #Wave equation #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.1080/14786435.2017.1283070
arxiv created 2016/06/24 · openalex created_date 2016/07/22 · openalex publication_date 2017/01/31 · arxiv updated 2018/02/23 · openalex updated_date 2026/08/05
Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with displacement-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson for describing longitudinal waves in biomembranes and later improved by Engelbrecht, Tamm and Peets taking into account the microinertia of a biomembrane. The steady solution in the form of a solitary wave is derived and the influence of nonlinear and dispersive terms over a large range of possible sets of coefficients demonstrated. The solutions emerging from arbitrary initial inputs are found using the numerical simulation. The properties of emerging trains of solitary waves are analysed. Finally, the interaction of solitary waves which satisfy the governing equation is studied. The interaction process is not fully elastic and after several interactions radiation effects may be significant. This means that for the present case the solitary waves are not solitons in the strict mathematical sense. However, like in other cases known in solid mechanics, such solutions may be conditionally called solitons.