Journal of Nonlinear Mathematical Physics

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 N for the short pulse equation, by the determinants of the eigenfunctions of its Lax pair. In the course of the derivation of N, 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. N 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 2
Pages
183 - 194
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2017.1306947How 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  - 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  -