中国物理B ›› 2023, Vol. 32 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/acd62c

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Trajectory equation of a lump before and after collision with other waves for generalized Hirota-Satsuma-Ito equation

Yarong Xia(夏亚荣)1,2,†, Kaikai Zhang(张开开)2, Ruoxia Yao(姚若侠)3,‡, and Yali Shen(申亚丽)4   

  1. 1 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
    2 School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
    3 School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;
    4 Maths and Information Technology School, Yuncheng University, Yuncheng 044000, China
  • 收稿日期:2023-04-13 修回日期:2023-05-10 接受日期:2023-05-17 出版日期:2023-09-21 发布日期:2023-10-08
  • 通讯作者: Yarong Xia, Ruoxia Yao E-mail:xiayarong2014@126.com;rxyao@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12001424 and 12271324), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JZ-21), the Chinese Post Doctoral Science Foundation (Grant No. 2020M673332), and the Three-year Action Plan Project of Xi'an University (Grant No. 2021XDJH01).

Trajectory equation of a lump before and after collision with other waves for generalized Hirota-Satsuma-Ito equation

Yarong Xia(夏亚荣)1,2,†, Kaikai Zhang(张开开)2, Ruoxia Yao(姚若侠)3,‡, and Yali Shen(申亚丽)4   

  1. 1 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
    2 School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
    3 School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;
    4 Maths and Information Technology School, Yuncheng University, Yuncheng 044000, China
  • Received:2023-04-13 Revised:2023-05-10 Accepted:2023-05-17 Online:2023-09-21 Published:2023-10-08
  • Contact: Yarong Xia, Ruoxia Yao E-mail:xiayarong2014@126.com;rxyao@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12001424 and 12271324), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JZ-21), the Chinese Post Doctoral Science Foundation (Grant No. 2020M673332), and the Three-year Action Plan Project of Xi'an University (Grant No. 2021XDJH01).

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摘要： Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of $m$-lump with $n$-soliton and $n$-breather wave for generalized Hirota-Satsuma-Ito (GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with $n$-soliton and $n$-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, it is revealed that collisions between the lump wave and other waves are elastic, the corresponding collision diagrams are used to further explain.

关键词: Hirota bilinear method, long wave limit, hybrid solutions, trajectory equation

Abstract: Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of $m$-lump with $n$-soliton and $n$-breather wave for generalized Hirota-Satsuma-Ito (GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with $n$-soliton and $n$-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, it is revealed that collisions between the lump wave and other waves are elastic, the corresponding collision diagrams are used to further explain.

Key words: Hirota bilinear method, long wave limit, hybrid solutions, trajectory equation

中图分类号:  (Partial differential equations)

  • 02.30.Jr
05.45.Yv (Solitons) 02.30.Ik (Integrable systems)