Exploring the data-driven soliton dynamics to the complex coupled Maccari system: application of the analytical–machine learning algorithm.
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| Title: | Exploring the data-driven soliton dynamics to the complex coupled Maccari system: application of the analytical–machine learning algorithm. |
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| Authors: | Muhammad, Jan1 (AUTHOR), Yao, Fengping2 (AUTHOR), Younas, Usman2 (AUTHOR) usmanalgebra@shu.edu.cn |
| Source: | Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Apr2026, Vol. 77 Issue 4, p1-26. 26p. |
| Subjects: | Solitons, Machine learning, Multilayer perceptrons, Wave analysis, Nonlinear theories, Scientific method, Nonlinear waves |
| Abstract: | In this paper, the (2+1)-dimensional complex coupled Maccari system is under investigation. This model is important for comprehending the propagation of waves through several types of physical systems, such as plasma physics, optical fiber communications, fluid dynamics, and nonlinear acoustics. In particular, the proposed system models the interaction between fast, short-wave fields and a slow, long-wave background, making it useful for describing wave dynamics in different areas. In this study, a combination of the analytical and machine learning framework is presented. In the first phase, the recently developed techniques such that modified Riccati extended simple equation methodology, the generalized Arnous technique, and the Kumar–Malik method are applied for extracting the variety of solutions. The solutions in the forms of bright, dark, combined solitons as well as periodic, hyperbolic, and exponential solutions are obtained. Then, in the second phase the obtained solutions are discussed by the application of the hybrid symbolic numeric framework based on multilayer perceptron regressor neural network. The framework accurately captures key soliton types as well as shows excellent convergence with analytical solutions, as evidenced by low error metrics. Moreover, the three-dimensional, two-dimensional, contour, training loss, error distribution, model predictive performance scatter plots are presented in the figures for the observing the performance of the applied techniques. This methodology effectively bridges the gap between traditional analytical techniques and modern machine learning, creating a unified platform for both constructing and simulating nonlinear wave dynamics. By validating the effectiveness of current methodologies and elucidating the nonlinear dynamic characteristics of the proposed model, this work substantially advances the disciplines of higher-dimensional nonlinear wave fields and nonlinear science. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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