Two-dimensional rogue wave clusters in self-focusing Kerr-media

WenYe Zhong, Pei Qin, Wei-Ping Zhong and Milivoj Belić

Chaos, Solitons & Fractals, 2022, vol. 165, issue P2

Abstract: In this paper we consider two-dimensional (2D) rogue waves that can be obtained from the approximate solution of the (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. The approximate method proposed in this paper not only reduces complex operations needed for the solution of high-dimensional nonlinear partial differential equations, but also furnishes an effective mechanism for constructing stable high-dimensional rogue wave clusters, and also provides for more abundant local rogue wave excitations. Such an investigation is important in view of the known tendency for instability of localized solutions to the 2D and 3D NLS equations with focusing Kerr nonlinearity. We adopt the (2 + 1)-dimensional NLS equation in cylindrical coordinates as the basic model, and reduce the complexity of its solution by looking for the radially-symmetric ring-like solutions with the specific feature that the radius of the ring L is much greater than the ring thickness w. In this manner, we obtain an approximate analytical solution with the separated radial and angular functions which depend on the two integer parameters, the azimuthal mode number m and the rogue wave solution's order number n. With the two parameters L and w also included in the approximate solution, we show the profiles of the first-order and the second-order rogue waves, and discuss their characteristics. The method for finding approximate rogue wave solutions of the (2 + 1)-dimensional NLS equation proposed in this paper can be used as an effective way to obtain higher-order rogue wave excitations, and can be extended to other (2 + 1)-dimensional nonlinear systems.

Keywords: Rogue wave; Nonlinear Schrödinger equation; Higher-order rogue wave excitations (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922010037
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:165:y:2022:i:p2:s0960077922010037

DOI: 10.1016/j.chaos.2022.112824

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. ().