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

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 relation...

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Bibliographic Details
Published in:Chinese physics B 2023-09, Vol.32 (9), p.90504-267
Main Authors: Chen, Mi, Wang, Zhen
Format: Article
Language:English
Subjects:
Hirota bilinear method
Riemann theta function
three-periodic solution
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Summary: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.
ISSN:1674-1056
DOI:10.1088/1674-1056/acd9c4