Novel soliton dynamics via (G′∕G)-expansion neural networks approach in the modified Camassa–Holm and Kuramoto–Sivashinsky models

This study investigates exact solitary wave solutions of the modified Camassa–Holm (mCH) and modified Kuramoto–Sivashinsky (mKS) equations, which are fundamental in fluid dynamics, nonlinear optics, and quantum mechanics. Solutions are obtained using the [Formula: see text]-expansion neural network analytical method, a hybrid approach that integrates the symbolic capability of neural networks (NNs) with [Formula: see text]-expansion method, enabling the direct construction of analytical exact solutions without relying on classical transformations. The method yields a rich variety of soliton structures in trigonometric, hyperbolic, and rational forms, including periodic, bright, dark, V-shaped, kink, and…