https://doi.org/10.1140/epjp/s13360-025-06567-8
Regular Article
Numerical simulation on multi-periodic wave solutions for the 
-dimensional generalized Nizhnik–Novikov–Veselov equation
1
School of Science, Shanghai Maritime University, 201306, Shanghai, People’s Republic of China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, People’s Republic of China
Received:
6
May
2025
Accepted:
19
June
2025
Published online:
3
July
2025
Studying periodic wave solutions is very important for revealing the universal wave phenomena in nonlinear systems. In this paper, we deal with the overdetermined systems arising in the search for multi-periodic wave solutions, by combining Akira Nakamura’s direct method for constructing N-periodic wave solutions with the Levenberg–Marquardt method. This approach enables us to obtain 2- and 3-periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation successfully.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
