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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 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 |
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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.
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Received: 13 April 2023
Revised: 10 May 2023
Accepted manuscript online: 17 May 2023
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PACS:
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02.30.Jr
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(Partial differential equations)
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05.45.Yv
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(Solitons)
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02.30.Ik
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(Integrable systems)
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| Fund: 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). |
Corresponding Authors:
Yarong Xia, Ruoxia Yao
E-mail: xiayarong2014@126.com;rxyao@snnu.edu.cn
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Cite this article:
Yarong Xia(夏亚荣), Kaikai Zhang(张开开), Ruoxia Yao(姚若侠), and Yali Shen(申亚丽) Trajectory equation of a lump before and after collision with other waves for generalized Hirota-Satsuma-Ito equation 2023 Chin. Phys. B 32 100201
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