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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 School of Mathematical Science, Dalian University of Technology, Dalian 116024, China;
2 School of Mathematical Science, Beihang University, Beijing 100191, China |
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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.
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Received: 05 April 2023
Revised: 17 May 2023
Accepted manuscript online: 30 May 2023
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PACS:
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05.45.Yv
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(Solitons)
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03.75.Lm
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(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
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02.30.Mv
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(Approximations and expansions)
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| Fund: 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 |
Corresponding Authors:
Zhen Wang
E-mail: wangzmath@163.com
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Cite this article:
Mi Chen(陈觅) and Zhen Wang(王振) Analytical three-periodic solutions of Korteweg-de Vries-type equations 2023 Chin. Phys. B 32 090504
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