Dynamics of Soliton Solutions to Nonlinear Coupled System with Neural Network and Chaotic Insights

Jan Muhammad, Ali H. Tedjani, Usman Younas () and Fengping Yao
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Jan Muhammad: Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China
Ali H. Tedjani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Usman Younas: Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China
Fengping Yao: Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China

Mathematics, 2025, vol. 13, issue 23, 1-31

Abstract: This study examines the nonlinear dynamical behavior of a Van der Waals system in the viscosity–capillarity regularization form. The solitary wave solutions of the proposed model are investigated using advanced analytical techniques, including the generalized Arnous method, the modified generalized Riccati equation mapping method, and the modified F-expansion approach. Additionally, we use mathematical simulations to enhance our comprehension of wave propagation. Moreover, a machine learning algorithm known as the multilayer perceptron regressor neural network was adopted to predict the performance results of our soliton solutions. Another important aspect of this study is the exploration of the chaos of the studied model by introducing a perturbed system. Chaotic analysis is supported by different techniques, such as return maps, power spectra, a bifurcation diagram, and a chaotic attractor. This multifaceted investigation not only emphasizes the rich dynamical pattern of the studied model but also presents a robust mathematical framework for studying nonlinear systems. The studied model also presents a robust mathematical framework for studying nonlinear systems. This study offers novel insights into nonlinear dynamics and wave phenomena by assessing the effectiveness of modern methodologies and clarifying the distinctive characteristics of a system’s nonlinear dynamics.

Keywords: analytical methods; Van der Waals system; machine learning; solitons; Galilean transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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