High-order doubly localized waves in (2+1)-dimensional Maccari system

doi:10.1088/1674-1056/ae0682

Abstract In this work, we explore the doubly localized wave solutions for the (2+1)-dimensional Maccari system using Hirota's bilinear method and Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions illustrate the temporal evolution of a line rogue wave and a lump in the background of a breather or homoclinic orbit. The line rogue wave in these solutions is characterized by two endpoints, and is thus referred to as a line-segment rogue wave. The lump is also a doubly localized wave known as a rogue lump, which is also localized in both time and two spatial dimensions. These waves emerge from the breather waves or homoclinic orbits and remain unchanged for a short period of time, eventually merging into other breather waves or homoclinic orbits. Notably, these rogue lumps appear and vanish alongside the homoclinic orbits and play a significant role in understanding extreme events in physical scenarios.

Keywords: Maccari system bilinear form Schur polynomial doubly localized wave homoclinic orbit

Received: 28 August 2025
Revised: 10 September 2025
Accepted manuscript online: 15 September 2025

PACS:	02.30.Ik	(Integrable systems)
	03.75.Nt	(Other Bose-Einstein condensation phenomena)
	02.30.Hq	(Ordinary differential equations)

Fund: The authors would like to thank the Editor and Reviewers for their valuable comments. Project supported by the Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications (Grant Nos. NY225085 and NY225004).

Corresponding Authors: Xue-Wei Yan
E-mail: xwyan16@163.com

Cite this article:

Xue-Wei Yan(严学威), Jin-Jin Mao(茆晋晋), and Min-Jie Dong(董敏杰) High-order doubly localized waves in (2+1)-dimensional Maccari system 2026 Chin. Phys. B 35 070201

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High-order doubly localized waves in (2+1)-dimensional Maccari system

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