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Title: Radiating solitary waves in coupled Boussinesq equations
Authors: Grimshaw, Roger H.J.
Khusnutdinova, Karima R.
Moore, Kieron R.
Keywords: Coupled Boussinesq equations
Radiating solitary waves
Perturbation theory
Issue Date: 2017
Publisher: © the Authors. Published by Oxford University Press
Citation: GRIMSHAW, R.H.J., KHUSNUTDINOVA, K.R. and MOORE, K.R., 2017. Radiating solitary waves in coupled Boussinesq equations. IMA Journal of Applied Mathematics, 82 (4), pp. 802–820.
Abstract: 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.
Description: This paper is closed access until 25th. May 2018
Version: Accepted for publication
DOI: 10.1093/imamat/hxx014
URI: https://dspace.lboro.ac.uk/2134/24858
Publisher Link: https://doi.org/10.1093/imamat/hxx014
ISSN: 0272-4960
Appears in Collections:Closed Access (Maths)

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