Computational modeling demonstrates accurate Gardner equation solutions using a hybrid neural network and Sardar sub-equation method, highlighting new integration pathways for nonlinear physics.
This study examines the Gardner equation, a fundamental nonlinear partial differential equation (PDE) used in modeling various physical phenomena, and wave motions. Hyperbolic and trigonometric analytical solutions are derived using the Sardar sub-equation method. Additionally, an artificial neural network (ANN) in combination with the Sardar sub-equation method, an analytical solution approach for the Gardner equation, is proposed. The results demonstrate that the ANN-based hybrid model predicted the Gardner equation solutions with accuracy. This study can be useful in the integration of classical analytical methods and the ANN-based approaches to solutions of nonlinear partial equations.
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Takımsu et al. (2026) studied this question.
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