A Novel Neural Network-Based Symbolic Approach for Shallow-Water Waves with Surface Tension

This paper examines the sixth-order generalized Boussinesq equation, which describes the dynamics of shallow-water waves, including the effects of surface tension. The study introduces Kudryashov’s R-function neural network approach for the first time, aiming to provide exact solutions to the nonlinear differential equation that represents the mathematical model of the sixth-order generalized Boussinesq equation. This technique incorporates the solutions of a nonlinear differential equation into neural networks, using them as an activation function within the hidden layer. In line with previous research on this topic, two categories of solutions are derived: solitary wave and shock wave solutions. Additionally, this paper includes 3D and 2D graphs to visually represent the solutions obtained.