Journal of Nonlinear Mathematical Physics

Volume 24, Issue 2, March 2017, Pages 195 - 209

A modified complex short pulse equation of defocusing type

Authors
Shoufeng Shen*
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, China,mathssf@zjut.edu.cn
Bao-Feng Feng
School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, TX, 78541, USA
Yasuhiro Ohta
Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
*Corresponding author.
Corresponding Author
Shoufeng Shen
Received 26 August 2016, Accepted 11 February 2017, Available Online 6 January 2021.
DOI
10.1080/14029251.2017.1306946How to use a DOI?
Keywords
Short pulse equation; hodograph transformation; dark soliton; Hirota’s bilinear method
Abstract

In this paper, we are concerned with a modified complex short pulse (mCSP) equation of defocusing type. Firstly, we show that the mCSP equation is linked to a complex coupled dispersionless equation of defocusing type via a hodograph transformation, thus, its Lax pair can be deduced. Then the bilinearization of the defocusing mCSP equation is formulated via dependent variable and hodograph transformations. One- and two-dark soliton solutions are found by Hirota’s bilinear method and their properties are analyzed. It is shown that, depending on the parameters, the dark soliton solution can be either smoothed, cusponed or looped one. More specifically, the dark soliton tends to be evolved into a singular (cusponed or looped) one due to the increase of the spatial wave number in background plane waves and the increase of the depth of the trough. In the last part of the paper, we derive the defocusing mCSP equation from the single-component extended KP hierarchy by the reduction method. As a by-product, the N-dark soliton solution in the form of determinants for the defocusing mCSP is provided.

Open Access

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 2
Pages
195 - 209
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2017.1306946How to use a DOI?
Open Access

TY  - JOUR
AU  - Shoufeng Shen
AU  - Bao-Feng Feng
AU  - Yasuhiro Ohta
PY  - 2021
DA  - 2021/01/06
TI  - A modified complex short pulse equation of defocusing type
JO  - Journal of Nonlinear Mathematical Physics
SP  - 195
EP  - 209
VL  - 24
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1306946
DO  - 10.1080/14029251.2017.1306946
ID  - Shen2021
ER  -