Bilinear Recurrent Neural Network for a Modified Benney-Luke Equation

• Published in: International journal of applied and computational mathematics Vol. 11; no. 2; p. 35
• Main Authors: Tuan, Nguyen Minh, Meesad, Phayung
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.04.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Science and Engineering; Exact solutions; Machine learning; Mathematical analysis; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Neural networks; Nonlinear differential equations; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Partial differential equations; Recurrent neural networks; Theoretical; Water waves; Wave propagation; Bilinear neural network method; BNNM; Exact analytic solution; Benney-Luke equation
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01851-8

Finding exact analytic solutions of nonlinear differential equations, one of the fields that are significantly important to mechanic engineering and dynamic systems, has been a focus in the past eras. The Benney-Luke equation representing the propagation of water wave surface is solved by many methods yielding diverse solutions. This paper presents a new extended form of the Benney-Luke equation and the exact analytic solutions are obtained using the bilinear neural network technique regarding the definition of Hirota bilinear form. The various solutions are established and produced by constructing activation functions consistent with the processing procedure. The solutions are depicted and compared in two and three dimensions to investigate the behaviors.