Volume 17, Issue 2, June 2010, Pages 197 - 211
Vadermonde-Type Odd-Soliton Solutions for the Whitham–Broer–Kaup Model in the Shallow Water Small-Amplitude Regime
Authors
Lei Wang*, Yi-Tian Gao*, †, ‡, Xiao-Ling Gai*, Xin Yu*, Zhi-Yuan Sun*
*Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
†State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Received 25 September 2009, Accepted 1 November 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000714How to use a DOI?
- Keywords
- Whitham–Broer–Kaup system; odd-soliton solutions; N-fold Darboux transformation; Vandermonde-like determinant; symbolic computation
- Abstract
Under investigation in this paper, with symbolic computation, is the Whitham–Broer–Kaup (WBK) system for the dispersive long waves in the shallow water small-amplitude regime. N-fold Darboux transformation (DT) for a spectral problem associated with the WBK system is constructed. Odd-soliton solutions in terms of the Vandermonde-like determinant for the WBK system are presented via the N-fold DT and evolution of the three-soliton solutions is graphically studied. Our results could be used to illustrate the bidirectional propagation of the waves in the shallow water small-amplitude regime.
- Copyright
- © 2010 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 - Lei Wang AU - Yi-Tian Gao AU - Xiao-Ling Gai AU - Xin Yu AU - Zhi-Yuan Sun PY - 2021 DA - 2021/01/07 TI - Vadermonde-Type Odd-Soliton Solutions for the Whitham–Broer–Kaup Model in the Shallow Water Small-Amplitude Regime JO - Journal of Nonlinear Mathematical Physics SP - 197 EP - 211 VL - 17 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000714 DO - 10.1142/S1402925110000714 ID - Wang2021 ER -