Volume 24, Issue 2, March 2017, Pages 183 - 194
The determinant representation of an N-fold Darboux transformation for the short pulse equation
Authors
Shuzhi Liu1, Lihong Wang2, Wei Liu3, Deqin Qiu, Jingsong He1, *
1Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P. R. China
2School of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, P. R. China
3College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, 264005, P. R. China
4College of Mathematics and Statistics, Jishou University, Hunan 416000, P. R. China
Corresponding Author
Jingsong He
Received 22 October 2016, Accepted 26 January 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1306947How to use a DOI?
- Keywords
- Darboux transformation; short pulse equation; soliton; hodograph transformation
- Abstract
We present an explicit representation of an N-fold Darboux transformation T̃N for the short pulse equation, by the determinants of the eigenfunctions of its Lax pair. In the course of the derivation of T̃N, we show that the quasi-determinant is avoidable, and it is contrast to a recent paper (J. Phys. Soc. Jpn. 81 (2012), 094008) by using this relatively new tool which was introduced to study noncommutative mathematical objectives. T̃N produces new solutions u[N] and x[N] which are expressed by ratios of two corresponding determinants. We also obtain the soliton solutions, which have a variable trajectory, of the short pulse equation from new “seed” solutions.
- 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 - Shuzhi Liu AU - Lihong Wang AU - Wei Liu AU - Deqin Qiu AU - Jingsong He PY - 2021 DA - 2021/01/06 TI - The determinant representation of an N-fold Darboux transformation for the short pulse equation JO - Journal of Nonlinear Mathematical Physics SP - 183 EP - 194 VL - 24 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1306947 DO - 10.1080/14029251.2017.1306947 ID - Liu2021 ER -