中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90504-090504.doi: 10.1088/1674-1056/acd9c4

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Analytical three-periodic solutions of Korteweg-de Vries-type equations

Mi Chen(陈觅)1 and Zhen Wang(王振)2,†   

  1. 1 School of Mathematical Science, Dalian University of Technology, Dalian 116024, China;
    2 School of Mathematical Science, Beihang University, Beijing 100191, China
  • 收稿日期:2023-04-05 修回日期:2023-05-17 接受日期:2023-05-30 发布日期:2023-09-01
  • 通讯作者: Zhen Wang E-mail:wangzmath@163.com
  • 基金资助:
    Project supported by the National National Science Foundation of China (Grant Nos. 52171251, U2106225, and Project supported by the National National Science Foundation of China (Grant Nos. 52171251, U2106225, and

Analytical three-periodic solutions of Korteweg-de Vries-type equations

Mi Chen(陈觅)1 and Zhen Wang(王振)2,†   

  1. 1 School of Mathematical Science, Dalian University of Technology, Dalian 116024, China;
    2 School of Mathematical Science, Beihang University, Beijing 100191, China
  • Received:2023-04-05 Revised:2023-05-17 Accepted:2023-05-30 Published:2023-09-01
  • Contact: Zhen Wang E-mail:wangzmath@163.com
  • Supported by:
    Project supported by the National National Science Foundation of China (Grant Nos. 52171251, U2106225, and Project supported by the National National Science Foundation of China (Grant Nos. 52171251, U2106225, and

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摘要： Based on the direct method of calculating the periodic wave solution proposed by Nakamura, we give an approximate analytical three-periodic solutions of Korteweg-de Vries (KdV)-type equations by perturbation method for the first time. Limit methods have been used to establish the asymptotic relationships between the three-periodic solution separately and another three solutions, the soliton solution, the one- and the two-periodic solutions. Furthermore, it is found that the asymptotic three-soliton solution presents the same repulsive phenomenon as the asymptotic three-soliton solution during the interaction.

关键词: Hirota bilinear method, Riemann theta function, three-periodic solution

Abstract: Based on the direct method of calculating the periodic wave solution proposed by Nakamura, we give an approximate analytical three-periodic solutions of Korteweg-de Vries (KdV)-type equations by perturbation method for the first time. Limit methods have been used to establish the asymptotic relationships between the three-periodic solution separately and another three solutions, the soliton solution, the one- and the two-periodic solutions. Furthermore, it is found that the asymptotic three-soliton solution presents the same repulsive phenomenon as the asymptotic three-soliton solution during the interaction.

Key words: Hirota bilinear method, Riemann theta function, three-periodic solution

中图分类号:  (Solitons)

  • 05.45.Yv
03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 02.30.Mv (Approximations and expansions)