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, [in press].
Advanced Structured Materials;103
Weakly-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.
This book chapter is closed access until 31 March 2021.
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.