Certain (2+1)-dimensional multi-soliton asymptotics in the shallow water

Xi-Hu Wu and Yi-Tian Gao

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: This paper investigates the Kadomtsev–Petviashvili I equation, which describes the variation of shallow-water wave amplitude in the transverse direction, making it applicable to the shallow water conditions with strong surface tension., e.g., in the capillary wave problems. With respect to the amplitude of a shallow-water-wave packet, we derive a binary Darboux transformation (DT), and then perform the asymptotic analysis on the N-soliton solutions to derive the algebraic expressions of the N soliton components, where N is a positive integer. The asymptotic results indicate the energy stability in the shallow-water soliton interactions under certain conditions. Additionally, each soliton component contributes to the phase shifts of the other soliton components. Taking N=3 as an example, we illustrate the 3 interacting solitons via the 3D plots and density plots, which align with our asymptotic-analysis results. Although the asymptotic analysis method used is confined to the binary-DT framework, this paper tries to apply such a method [traditionally used in the (1+1)-dimensional systems] to the aforementioned (2+1)-dimensional system. Our analysis, which still needs to be confirmed by the relevant numerical simulation and experiments, might offer some explanations for the complex and variable natural mechanisms of the real-world shallow water waves.

Keywords: Shallow water; Kadomtsev–Petviashvili I equation; Soliton interaction; Asymptotic analysis (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924010129
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010129

DOI: 10.1016/j.chaos.2024.115460

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().