2134/24858
Roger Grimshaw
Karima Khusnutdinova
Kieron R. Moore
Radiating solitary waves in coupled Boussinesq equations
2017
Loughborough University
Coupled Boussinesq equations
Radiating solitary waves
Perturbation theory
2017-04-28 15:27:19
article
https://repository.lboro.ac.uk/articles/Radiating_solitary_waves_in_coupled_Boussinesq_equations/9388808
In this paper we are concerned with the analytical description of radiating solitary wave solutions of coupled regularised Boussinesq equations. This type of solution consists of a leading solitary wave with a small-amplitude co-propagating oscillatory tail, and emerges from a pure solitary wave solution of a symmetric reduction of the full system. We construct an asymptotic solution, where the leading order approximation in both components is obtained as a particular solution of the regularised Boussinesq equations in the symmetric case. At the next order, the system uncouples into two linear non-homogeneous ordinary differential equations with variable coefficients, one correcting the localised part of the solution, which we find analytically, and the other describing the co-propagating oscillatory tail. This latter equation is a fourth order ordinary differential equation and is solved approximately by two different methods, each exploiting the assumption that the leading solitary wave has a small
amplitude, and thus enabling an explicit estimate for the amplitude of the oscillating tail. These estimates are compared with corresponding numerical simulations.