中国物理B ›› 2026, Vol. 35 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/ae0435

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Integrable decompositions and superposed nonlinear solutions of (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Yan Li(李岩)1, Ruoxia Yao(姚若侠)1,†, and Senyue Lou(楼森岳)2   

  1. 1 School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi'an 710119, China;
    2 School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
  • 收稿日期:2025-07-21 修回日期:2025-09-05 接受日期:2025-09-08 发布日期:2026-04-01
  • 通讯作者: Ruoxia Yao E-mail:rxyao@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12501333 and 12271324), the Natural Science Basic Research Program of Shaanxi Province,China (Grant No. 2024JC-YBQN-0069), the China Postdoctoral Science Foundation (Grant No. 2024M751921), the 2023 Shaanxi Province Postdoctoral Research Project (Grant No. 2023BSHEDZZ186), and the Fundamental Research Funds for the Central Universities (Grant No. GK202304028).

Integrable decompositions and superposed nonlinear solutions of (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Yan Li(李岩)1, Ruoxia Yao(姚若侠)1,†, and Senyue Lou(楼森岳)2   

  1. 1 School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi'an 710119, China;
    2 School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
  • Received:2025-07-21 Revised:2025-09-05 Accepted:2025-09-08 Published:2026-04-01
  • Contact: Ruoxia Yao E-mail:rxyao@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12501333 and 12271324), the Natural Science Basic Research Program of Shaanxi Province,China (Grant No. 2024JC-YBQN-0069), the China Postdoctoral Science Foundation (Grant No. 2024M751921), the 2023 Shaanxi Province Postdoctoral Research Project (Grant No. 2023BSHEDZZ186), and the Fundamental Research Funds for the Central Universities (Grant No. GK202304028).

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摘要： The phenomenon of shallow water waves in nature attracts the attention of scholars and plays an important role in fields such as marine ecology, tidal waves, solitary waves, and offshore engineering. To better understand the phenomenon of shallow water waves, we investigate the $(2+1)$-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (2D-CDGKS) equation from the perspective of integrable decomposition. By utilizing the Lax pairs and formal variable separation (FVS) method, the 2D-CDGKS equation can be decomposed into the Sharma-Tasso-Olver (STO) equation, the integrable Svinolupov-Sokolov (SS) equation, and the Sawada-Kotera (SK) equation. We construct some novel exact solutions by linear superposing the integrable decomposition relations. Additionally, the superposition of two-soliton solution with three-soliton solution, two-soliton solution propagating on periodic cnoidal background waves, and soliton-cnoidal wave interaction solutions with interesting dynamics, are explored. Our results have important significance for understanding of the physical events consolidate the complex system under consideration and offering vital insights into the intricate dynamics of its behavior. Furthermore, the present work will enrich the investigation of nonlinear dynamics in high-dimensional nonlinear system, and provide theoretical support for the related experimental phenomena.

关键词: (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation, integrable decomposition, linear superposed solutions, nonlinear wave interaction

Abstract: The phenomenon of shallow water waves in nature attracts the attention of scholars and plays an important role in fields such as marine ecology, tidal waves, solitary waves, and offshore engineering. To better understand the phenomenon of shallow water waves, we investigate the $(2+1)$-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (2D-CDGKS) equation from the perspective of integrable decomposition. By utilizing the Lax pairs and formal variable separation (FVS) method, the 2D-CDGKS equation can be decomposed into the Sharma-Tasso-Olver (STO) equation, the integrable Svinolupov-Sokolov (SS) equation, and the Sawada-Kotera (SK) equation. We construct some novel exact solutions by linear superposing the integrable decomposition relations. Additionally, the superposition of two-soliton solution with three-soliton solution, two-soliton solution propagating on periodic cnoidal background waves, and soliton-cnoidal wave interaction solutions with interesting dynamics, are explored. Our results have important significance for understanding of the physical events consolidate the complex system under consideration and offering vital insights into the intricate dynamics of its behavior. Furthermore, the present work will enrich the investigation of nonlinear dynamics in high-dimensional nonlinear system, and provide theoretical support for the related experimental phenomena.

Key words: (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation, integrable decomposition, linear superposed solutions, nonlinear wave interaction

中图分类号:  (Integrable systems)

  • 02.30.Ik
02.30.Jr (Partial differential equations) 04.30.Nk (Wave propagation and interactions)