Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves Karima Khusnutdinova Matthew R. Tranter 2134/36514 https://repository.lboro.ac.uk/articles/chapter/Weakly-nonlinear_solution_of_coupled_Boussinesq_equations_and_radiating_solitary_waves/9377345 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. 2019-01-09 09:33:24 Coupled Boussinesq equations Coupled Ostrovsky equations Multiple-scales expansions Averaging Radiating solitary waves Mathematical Sciences not elsewhere classified