ArticleScientific reports2025
Exploring the exact solutions to the nonlinear systems with neural networks method.
Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Analytical methods and Riccati neural networks method of Kudryashov's quintuple self-phase modulation with dual-form of generalized nonlocal nonlinearity.Scientific reports · 2026Article
- On certain novel numerical and analytical solutions for the pure-cubic Schrödinger equation in optical fibers with Kerr nonlinearity.Scientific reports · 2026Article
- Soliton dynamics and stability analysis of a double-chain DNA model with various chaos detection tools.Scientific reports · 2025Article
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4 authors.
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Abstract
This paper explores the use of Riccati subequation neural networks to solve nonlinear partial differential equations modeling complex biological processes like cancer, brain function, and wound healing. These equations involve spatially varying biochemical signaling and tissue regeneration. The study applies a method where solutions to the Riccati problem are integrated into neural networks, with the first hidden layer neurons specifically providing the solution to the Riccati equation. Exact solutions for differential equations may be obtained using the suggested approach. In order to verify the mathematical foundation of this technique, we examine the proposed equations, which leads to the derivation of hyperbolic function solutions, trigonometric function solutions, and rational solutions. Using various graphical illustrations, the dynamic properties of certain solutions associated with waves have been demonstrated. The results provided in this study have the potential to improve understanding of the nonlinear dynamic characteristics displayed by the specified system and to confirm the effectiveness of the techniques that have been implemented.
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