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Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves
chapter
posted on 2019-01-09, 09:33 authored by Karima KhusnutdinovaKarima Khusnutdinova, Matthew R. TranterWeakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in which case the system can support radiating solitary waves. We construct a weakly-nonlinear d'Alembert-type solution of this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. Asymptotic validity of the solution is carefully examined numerically. We also discuss the limiting case of an infinite interval for localised initial conditions. The solution is applied to study interactions of radiating solitary waves.
Funding
KRK is grateful to the UK QJMAM Fund for Applied Mathematics for the support of her travel to the ESMC2018 in Bologna, Italy where some of these discussions have taken place. MRT is grateful to the UK Institute of Mathematics and its Applications and the London Mathematical Society for supporting travel to the same conference.
History
School
- Science
Department
- Mathematical Sciences
Published in
Dynamical Processes in Generalized Continua and StructuresPages
321-343Citation
KHUSNUTDINOVA, K.R. and TRANTER, M.R, 2019. Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves. IN: Altenbach, H. ... et al (eds). Dynamical Processes in Generalized Continua and Structures. Springer, pp. 321-343.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This is a pre-copyedited version of a contribution published in Altenbach, H. ... et al (eds). Dynamical Processes in Generalized Continua and Structures published by Springer. The definitive authenticated version is available online via http://doi.org/10.1007/978-3-030-11665-1Publication date
2019-03-19ISBN
9783030116644ISSN
1869-8433Publisher version
Book series
Advanced Structured Materials;103Language
- en