Best Paper Award
Güldem Yıldız
Nigde Omer Halisdemir University
Güldem Yıldız of Nigde Omer Halisdemir University, Turkey, is associated with the 2026 research article Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model, published by MDPI. The study concerns the Mathematics subject area and combines an analytical sub-equation technique with a hybrid artificial neural network framework. The supplied publication record reports 192 article views and 40 references. The research is presented in connection with the Best Paper Award category of the Global Best Achievements Awards.
Abstract
This article presents the academic recognition of Güldem Yıldız for research on solving the Gardner equation through the Sardar Sub-Equation Method and a hybrid artificial neural network model. The work addresses an analytical and computational treatment of a nonlinear mathematical equation, combining a sub-equation approach with neural-network-based modeling. Such a hybrid framework connects symbolic solution techniques with data-driven approximation, offering a structured basis for examining nonlinear wave equations and related mathematical behavior. The research was published by MDPI in 2026 and is associated with the Mathematics subject area. This page summarizes the researcher, scientific context, methodology, contributions, and recognition academically.
Keywords
Keywords: Gardner equation; Sardar Sub-Equation Method; artificial neural networks; hybrid computational model; nonlinear equations; mathematical physics; analytical solutions; Mathematics.
Introduction to the Research Topic
The Gardner equation is a nonlinear partial differential equation studied in mathematical physics. Analytical methods can provide explicit solution forms, while computational learning approaches can approximate relationships. The reported study combines the Sardar Sub-Equation Method with a hybrid artificial neural network model, linking analytical and computational perspectives in nonlinear research. [1]
Research Profile
Güldem Yıldız is affiliated with Nigde Omer Halisdemir University, Turkey, and is represented in Scopus by Author ID 55735455100 and in ORCID by 0000-0002-8120-3525. The supplied research record identifies Mathematics as the subject area, with six documents, seventeen citations, and an h-index of one at the time of this profile. [2] [3]
Scientific Background
The Gardner equation extends nonlinear wave models by incorporating nonlinear effects, making its solution structure relevant to applied mathematics and mathematical physics. Sub-equation methods seek tractable analytical forms, whereas artificial neural networks provide computational approximation. Combining these perspectives can support comparison between explicit solutions and learned representations for nonlinear research. [1]
Methodology
The approach uses the Sardar Sub-Equation Method to construct analytical solutions of the Gardner equation, followed by a hybrid artificial neural network model computationally. The methodology connects symbolic derivation with numerical or learning-based approximation. The article title establishes this methodological combination, while implementation should be verified in the published article. [1]
Key Findings
The study addresses the Gardner equation through a sub-equation solution method and a hybrid artificial neural network model. This combination indicates an emphasis on complementary analytical and computational treatment rather than one technique. Solution families, numerical results, training procedures, and error measures should be taken directly from the article carefully. [1]
Scientific Contributions
The contribution described by the title is the integration of the Sardar Sub-Equation Method with a hybrid artificial neural network framework for the Gardner equation. This approach connects established analytical solution techniques with computational learning. The work provides context for comparing symbolic formulations and model-based approximations in nonlinear mathematical analysis. [1]
Conclusion
The recognized research focuses on a hybrid treatment of the Gardner equation that combines an analytical sub-equation method with artificial neural network modeling. Its publication in 2026 places the work within current mathematical research. Further assessment of solution accuracy, generalization, and comparative performance requires consultation of the complete published study. [1]
External Links
References
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- MDPI. (2026). Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model. Symmetry.
https://doi.org/10.3390/sym18091479
- Elsevier. (n.d.). Scopus author details: Güldem Yıldız, Author ID 55735455100. Scopus.
https://www.scopus.com/authid/detail.uri?authorId=55735455100
- ORCID. (n.d.). Güldem Yıldız, ORCID iD 0000-0002-8120-3525. ORCID.
https://orcid.org/0000-0002-8120-3525