中国物理B ›› 2025, Vol. 34 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/ada54e

• • 上一篇    

Riemann-Hilbert approach to the higher-order Kaup-Newell equation on the half line

Hui Yu(于慧)1 and Ning Zhang(张宁)1,2,†   

  1. 1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    2 Department of Fundamental Course, Shandong University of Science and Technology, Taian 271019, China
  • 收稿日期:2024-11-02 修回日期:2024-12-10 发布日期:2025-02-18
  • 通讯作者: Ning Zhang E-mail:skd991310@sdust.edu.cn

Riemann-Hilbert approach to the higher-order Kaup-Newell equation on the half line

Hui Yu(于慧)1 and Ning Zhang(张宁)1,2,†   

  1. 1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    2 Department of Fundamental Course, Shandong University of Science and Technology, Taian 271019, China
  • Received:2024-11-02 Revised:2024-12-10 Published:2025-02-18
  • Contact: Ning Zhang E-mail:skd991310@sdust.edu.cn

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摘要： The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line. We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem. The jump matrix for this problem is derived from the spectral matrix, which is calculated based on both the initial conditions and the boundary conditions. The jump matrix is explicitly dependent and expressed through the spectral functions, which are derived from the initial and boundary information, respectively. These spectral functions are interdependent and adhere to a so-called global relationship.

关键词: higher-order Kaup-Newell equation, Fokas unified method, Riemann-Hilbert problem

Abstract: The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line. We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem. The jump matrix for this problem is derived from the spectral matrix, which is calculated based on both the initial conditions and the boundary conditions. The jump matrix is explicitly dependent and expressed through the spectral functions, which are derived from the initial and boundary information, respectively. These spectral functions are interdependent and adhere to a so-called global relationship.

Key words: higher-order Kaup-Newell equation, Fokas unified method, Riemann-Hilbert problem

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Ik (Integrable systems) 02.30.Zz (Inverse problems)