New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

DOI

10.1080/14029251.2017.1282248How to use a DOI?

Keywords

Soliton interactions; Whitham-Broer-Kaup system; asymptotic analysis; double Wronskian

Abstract

In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new double Wronskian functions as t → ±∞, we make a complete characterization of asymptotic solitons for the non-singular, non-trivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fully-resonant multi-soliton configurations, in each of which the amplitudes, velocities and numbers of asymptotic solitons are in general not equal as t → ±∞. To illustrate, we present the figures for several examples of soliton interactions occurring in the WBK system.

Copyright

© 2017 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Tao Xu
AU  - Changjing Liu
AU  - Fenghua Qi
AU  - Chunxia Li
AU  - Dexin Meng
PY  - 2021
DA  - 2021/01/06
TI  - New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 116
EP  - 141
VL  - 24
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1282248
DO  - 10.1080/14029251.2017.1282248
ID  - Xu2021
ER  -