https://doi.org/10.1140/epjp/s13360-023-04518-9
Regular Article
Analytical three-periodic solution and interaction for nonlocal Boussinesq equation
1
School of Mathematical Science, Dalian University of Technology, 116024, Dalian, China
2
School of Mathematical Science, Beihang University, 100191, Beijing, China
Received:
4
April
2023
Accepted:
16
September
2023
Published online:
8
October
2023
Based on a multidimensional Riemann 
function and the coupled Hirota bilinear system, we use the Perturbation method to construct the asymptotic analytical three-periodic solution of the nonlocal Boussinesq equation. The analytical three-periodic solution is a direct generalization of the one- and two-periodic solutions and it has 6 fundamental periods. To prove that this analytical solution is correct, we verify it with numerical results obtained by the Gauss-Newton method. In addition, the asymptotic relationship between the periodic solution and soliton solution is established by a small-amplitude limit method. Interestingly, we find that when the three-periodic solution has a local maximum, its asymptotic three-soliton solution has a global maximum. During the nonlinear interaction, both the three-periodic solution and its asymptotic soliton can exhibit repulsive phenomenon, respectively.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
