Rich spectrum of data-driven soliton phenomena by using the advanced artificial neural networking

Muhammad Zafarullah Baber, Fengping Yao and Muhammad Qasim

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: In this article, novel soliton solutions are examined for the generalized (2+1)-dimensional soliton equation. These solutions are constructed using an advanced improved bilinear neural network method. The Hirota bilinear form of the governing equation is derived, and neural network architectures with single-, double and three-hidden layers are employed. Single-hidden-layer architectures yield a variety of novel soliton phenomena, including M-lump, lump interaction-I, lump interaction-II, Bright–Dark, and double-periodic lump solutions. A double-hidden-layer architecture yields the interaction wave solution and three layer Interaction of periodic and breather waves solution. Moreover, the Levenberg–Marquardt artificial neural network method is used to check the validity and convergence of the obtained solutions. The fitness curves, regression, mean-squared error performance, transition-state, and error histogram plots are generated, clearly demonstrating the accuracy of solutions. 3D, contour, and 2D plots depict the physical behaviors of the constructed solutions. The extracted results are important for modeling and explaining different phenomena in ocean waves, atmospheric dynamics, magnetic confinement fusion, and space plasma.

Keywords: Soliton solutions; Hirota bilinear form; Dependent-variable transformation; Improved neural networking; Symbolic computation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008775

DOI: 10.1016/j.chaos.2026.118736

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