Journal of Nonlinear Mathematical Physics

Volume 28, Issue 1, March 2021, Pages 14 - 26

On the Coupled Dispersionless-type Equations and the Short Pulse-type Equations

Authors
Juan Hu1, Jia-Liang Ji2, Guo-Fu Yu3, *
1Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, P. R. China
2School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai, 201620, P. R. China
3School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
*Corresponding author. Email: gfyu@sjtu.edu.cn
Corresponding Author
Guo-Fu Yu
Received 25 July 2019, Accepted 28 February 2020, Available Online 10 December 2020.
DOI
https://doi.org/10.2991/jnmp.k.200922.002How to use a DOI?
Keywords
Short pulse equation, coupled integrable dispersionless equations, sine-Gordon equation, AKNS
Abstract

In this paper, we study the correspondence between the Coupled Dispersionless (CD)-type equations and the Short Pulse (SP)-type equations. From the real and complex modified CD equations, we construct the real and complex Modified Short Pulse (mSP) equations geometrically and algebraically. From the geometric point of view, we establish the link of the motions of space curves to the real and complex modified CD equations, then to the real and complex mSP equations via hodograph transformations. The integrability of these equations are confirmed by constructing their Lax pairs geometrically. By using hodograph transformation, we construct the two-component SP equation from the CD-type equations, the multi-component real and complex SP and mSP equations from the multi-component CD equations. The multi-soliton solutions in the determinant form for the mSP and two-component SP equations are provided.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
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
28 - 1
Pages
14 - 26
Publication Date
2020/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.200922.002How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
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  - Juan Hu
AU  - Jia-Liang Ji
AU  - Guo-Fu Yu
PY  - 2020
DA  - 2020/12
TI  - On the Coupled Dispersionless-type Equations and the Short Pulse-type Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 14
EP  - 26
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.002
DO  - https://doi.org/10.2991/jnmp.k.200922.002
ID  - Hu2020
ER  -