WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 21, 2026
On Deploying Bilinear Neural Network Method to Various Solutions of
(3+1)-dimensional Potential Yu-Toda-Sasa-Fukuyama Equation
Authors: , , , ,
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Abstract: This paper investigates the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation
using the Bilinear Neural Network Method (BNNM). This novel hybrid framework integrates Hirotas bilinear
formalism with neural network modeling. By reformulating the YTSF equation into its bilinear form and
embedding this structure into the BNNM architecture, multiple classes of exact analytical solutions are derived,
including kink-type, periodic, and rational forms. The proposed method yields closed-form solutions that
preserve mathematical rigor while improving computational efficiency for high-dimensional nonlinear evolution
equations. The results demonstrate the effectiveness of the BNNM in generating diverse solution structures for the
YTSF equation, providing potential applications in fluid dynamics, plasma physics, and other nonlinear physical
models.
Keywords:
(3+1)-dimensional YTSF equation, Bilinear Neural Network Method (BNNM), Hirota bilinear
form, nonlinear partial differential equations, exact solutions
Pages: 95-102
DOI: 10.37394/23203.2026.21.10