中国物理B ›› 2026, Vol. 35 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/ae0682

• •    下一篇

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

Xue-Wei Yan(严学威)1,†, Jin-Jin Mao(茆晋晋)1, and Min-Jie Dong(董敏杰)2   

  1. 1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
    2 School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China
  • 收稿日期:2025-08-28 修回日期:2025-09-10 接受日期:2025-09-15 发布日期:2026-07-15
  • 通讯作者: Xue-Wei Yan E-mail:xwyan16@163.com
  • 基金资助:
    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).

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

Xue-Wei Yan(严学威)1,†, Jin-Jin Mao(茆晋晋)1, and Min-Jie Dong(董敏杰)2   

  1. 1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
    2 School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China
  • Received:2025-08-28 Revised:2025-09-10 Accepted:2025-09-15 Published:2026-07-15
  • Contact: Xue-Wei Yan E-mail:xwyan16@163.com
  • Supported by:
    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).

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摘要： 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.

关键词: Maccari system, bilinear form, Schur polynomial, doubly localized wave, homoclinic orbit

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.

Key words: Maccari system, bilinear form, Schur polynomial, doubly localized wave, homoclinic orbit

中图分类号:  (Integrable systems)

  • 02.30.Ik
03.75.Nt (Other Bose-Einstein condensation phenomena) 02.30.Hq (Ordinary differential equations)