Data-Driven Soliton Modeling in Conformable Coupled Dispersionless Systems Using Jacobi Elliptic Functions and Bayesian-Regularized Neural Networks

The primary objective of this work is to investigate the complex dynamics of coupled dis-persionless equations formulated with the conformable derivative. Exact soliton solutions are first derived using the Jacobi elliptic function expansion method. These solutions are then used to train a data-driven model based on a Bayesian regularization-backpropagation neural network. The trained network is evaluated against the exact solutions through visual comparison using surface plots, contour plots, and corresponding error graphs. Furthermore, statistical metrics are computed for varying values of the conformable derivative parameter to assess prediction accuracy and robustness. The close agreement between predicted and exact solutions confirms the effectiveness of the proposed data-driven approach. This study highlights the potential of integrating analytical soliton solutions with neural network models for modeling nonlinear systems involving conformable derivatives.