New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions
- https://doi.org/10.1080/14029251.2017.1282248How to use a DOI?
- Soliton interactions, Whitham-Broer-Kaup system, asymptotic analysis, double Wronskian
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.
- © 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 -