2018/10/31 by К. Р. Хуснутдинова, K. R. Khusnutdinova, Khusnutdinova, K. R. +2
Computer Science · Physics and Astronomy · #Classical Physics (physics.class-ph) #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1810.13358
21 pages, 6 figures
arxiv created 2018/10/31 · openalex publication_date 2018/10/31 · arxiv updated 2018/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.