Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability
Article
Article Title | Solitons and lumps in the cylindrical |
---|---|
ERA Journal ID | 87 |
Article Category | Article |
Authors | Hu, Wencheng, Zhang, Zhao, Guo, Qi and Stepanyants, Yury |
Journal Title | Chaos: an interdisciplinary journal of nonlinear science |
Journal Citation | 34 (1) |
Article Number | 013138 |
Number of Pages | 15 |
Year | 2024 |
Publisher | AIP Publishing |
Place of Publication | United States |
ISSN | 1054-1500 |
1089-7682 | |
Digital Object Identifier (DOI) | https://doi.org/10.1063/5.0175696 |
Web Address (URL) | https://pubs.aip.org/aip/cha/article/34/1/013138/3130824/Solitons-and-lumps-in-the-cylindrical-Kadomtsev |
Abstract | We revise soliton and lump solutions described by the cylindrical Kadomtsev-Petviashvili (cKP) equation and construct new exact solutions relevant to physical observation. In the first part of this study, we consider basically axisymmetric waves described by the cylindrical Kortweg-de Vries equation and analyze approximate and exact solutions to this equation. Then, we consider the stability of the axisymmetric solitons with respect to the azimuthal perturbations and suggest a criterion of soliton instability. The results of our numerical modeling confirm the suggested criterion and reveal lump emergence in the course of the development of the modulation instability of ring solitons in the unstable case. In the next part of this study, which will follow shortly, we will present exact solutions to the cKP equation describing weakly nonlinear waves in media with positive dispersion subject to the modulation instability of solitons with respect to small azimuthal perturbations. |
Keywords | Kadomtsev-Petviashvili equation, soliton, lump, lump chain, modulation instability |
Contains Sensitive Content | Does not contain sensitive content |
ANZSRC Field of Research 2020 | 510399. Classical physics not elsewhere classified |
490199. Applied mathematics not elsewhere classified | |
Public Notes | This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 34, 013138 (2024) and may be found at https://doi.org/10.1063/5.0175696 |
Byline Affiliations | Zhongyuan University of Technology, China |
South China Normal University, China | |
School of Mathematics, Physics and Computing | |
Nizhny Novgorod State Technical University, Russia |
https://research.usq.edu.au/item/z4v87/solitons-and-lumps-in-the-cylindrical-kadomtsev-petviashvili-equation-i-axisymmetric-solitons-and-their-stability
Restricted files
Published Version
51
total views1
total downloads0
views this month0
downloads this month