A modified complex short pulse equation of defocusing type

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.

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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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  -