Journal of Nonlinear Mathematical Physics

Volume 24, Issue 1, December 2016, Pages 116 - 141

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

Authors
Tao Xu*
College of Science, China University of Petroleum, Beijing 102249, China, xutao@cup.edu.cn
Changjing Liu
College of Science, China University of Petroleum, Beijing 102249, China, 465930101@qq.com
Fenghua Qi
School of Information, Beijing Wuzi University, Beijing 101149, China, qifenghua434@163.com
Chunxia Li
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China, trisha_li2001@163.com
Dexin Meng
College of Science, China University of Petroleum, Beijing 102249, China, mdx3118@163.com
*Corresponding author.
Corresponding Author
Tao Xu
Received 13 August 2016, Accepted 1 January 2017, Available Online 6 January 2021.
DOI
https://doi.org/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 1
Pages
116 - 141
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1282248How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Tao Xu
AU  - Changjing Liu
AU  - Fenghua Qi
AU  - Chunxia Li
AU  - Dexin Meng
PY  - 2021
DA  - 2021/01
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  - https://doi.org/10.1080/14029251.2017.1282248
ID  - Xu2021
ER  -