https://doi.org/10.1140/epjs/s11734-025-01856-w
Regular Article
Neural network-enhanced bilinear framework for analytical soliton dynamics and wave interactions in (3+1)-dimensional Hirota–Satsuma–Ito system
School of Applied Science, Beijing Information Science and Technology University, 100192, Beijing, China
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
17
March
2025
Accepted:
8
August
2025
Published online:
21
August
2025
Abstract
In order to further investigate soliton dynamics in nonlinear systems, a bilinear neural network approach based on generalized bilinear transformations is proposed for the first time to study (3+1)-dimensional Hirota–Satsuma–Ito equation in this paper. By assignment activation function and arbitrary activation function, a neural network model with a single hidden layer, a double hidden layer, and three hidden layers is constructed, and the corresponding test functions are generated. After substituting the test function into the generalized bilinear form of the Hirota–Satsuma–Ito equation, various solutions are derived using symbolic computational Maple, including soliton solution, periodic solution, interferometric wave interaction solution, and so on. Analyzed the dynamic characteristics and features of different soliton waves. These findings may contribute to the practical application of soliton dynamics in fields such as communication, data transmission, and nonlinear optics.
Copyright comment 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.
© The Author(s), under exclusive licence to EDP Sciences, 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.
