中国物理B ›› 2025, Vol. 34 ›› Issue (11): 110502-110502.doi: 10.1088/1674-1056/ae1019

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Periodic lump, soliton, and some mixed solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equations

Xiao-Min Wang(王晓敏)1,2,†, Ji Li(李吉)1,2, and Xiao-Xiao Hu(胡霄骁)3   

  1. 1 Department of Physics, Taiyuan Normal University, Jinzhong 030619, China;
    2 Institute of Computational and Applied Physics, Taiyuan Normal University, Jinzhong 030619, China;
    3 Shanxi Chinese Medicine School, Shanxi Health Vocational University, Taiyuan 030012, China
  • 收稿日期:2025-07-15 修回日期:2025-09-29 接受日期:2025-10-07 发布日期:2025-11-13
  • 通讯作者: Xiao-Min Wang E-mail:wangxiaomin086@163.com
  • 基金资助:
    This work was supported by the Applied Basic Research Program of Shanxi Province, China (Grant Nos. 202403021212253 and 202203021221217).

Periodic lump, soliton, and some mixed solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equations

Xiao-Min Wang(王晓敏)1,2,†, Ji Li(李吉)1,2, and Xiao-Xiao Hu(胡霄骁)3   

  1. 1 Department of Physics, Taiyuan Normal University, Jinzhong 030619, China;
    2 Institute of Computational and Applied Physics, Taiyuan Normal University, Jinzhong 030619, China;
    3 Shanxi Chinese Medicine School, Shanxi Health Vocational University, Taiyuan 030012, China
  • Received:2025-07-15 Revised:2025-09-29 Accepted:2025-10-07 Published:2025-11-13
  • Contact: Xiao-Min Wang E-mail:wangxiaomin086@163.com
  • Supported by:
    This work was supported by the Applied Basic Research Program of Shanxi Province, China (Grant Nos. 202403021212253 and 202203021221217).

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摘要： The (2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper, which describe optical solitons in birefringent fibers. Utilizing the Hirota bilinear method, we system-atically construct single- and double-periodic lump solutions. To provide a detailed insight into the dynamic behavior of the nonlinear waves, we explore diverse mixed solutions, including bright-dark, W-shaped, multi-peak, and bright soliton solutions. Building upon single-periodic lump solutions, we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method. Moreover, we obtain the interaction solutions involving lumps, periodic lumps, and solitons. The interactions among two solitons, multiple lumps, and mixed waves are illustrated and analyzed. Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones. These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.

关键词: nonlinear Schrödinger equations, lump solutions, mixed solutions, Hirota bilinear method

Abstract: The (2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper, which describe optical solitons in birefringent fibers. Utilizing the Hirota bilinear method, we system-atically construct single- and double-periodic lump solutions. To provide a detailed insight into the dynamic behavior of the nonlinear waves, we explore diverse mixed solutions, including bright-dark, W-shaped, multi-peak, and bright soliton solutions. Building upon single-periodic lump solutions, we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method. Moreover, we obtain the interaction solutions involving lumps, periodic lumps, and solitons. The interactions among two solitons, multiple lumps, and mixed waves are illustrated and analyzed. Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones. These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.

Key words: nonlinear Schrödinger equations, lump solutions, mixed solutions, Hirota bilinear method

中图分类号:  (Solitons)

  • 05.45.Yv
02.70.Wz (Symbolic computation (computer algebra)) 87.10.Ed (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)