Neural network-based computational analysis of pressure-driven nonlinear waves in gas-liquid mixtures and oil transportation pipelines.

In this work, we develop a computational approach for the analytical investigation of the dynamics of waves in a nonlinear system described by the Kudryashov-Sinelshchikov equation which is a nonlinear partial differential equation of (1+1) dimensions that models the propagation of pressure waves in bubbly liquids, multiphase flow systems, oil pipeline transport, and nonlinear acoustics. In the suggested approach, we use the combination of a multilayer feedforward artificial neural network and the Riccati sub-equation method where an exact solution to the Riccati auxiliary equation is used as an activation function of the hidden layer. In contrast to typical data-driven artificial neural networks, the unknown neural network parameters are calculated analytically by means of symbolic computations, and there is no need for training or optimization procedures. The validity of the solutions is checked by the direct substitution in the governing equation, while the properties of the solutions are analyzed with the help of two, three, and contour plots constructed in Wolfram Mathematica. In addition, modulation instability analysis is carried out to study the effect of small perturbation on the continuous wave solutions, and it is found that there is no exponential instability in the solutions obtained. The suggested neural network-inspired theoretical model serves as a computationally effective tool for finding exact solutions of nonlinear evolution equations.