Wave dynamics of Data-Driven soliton interaction for the nonlinear Bubble liquid model in complex fluid systems using Symbolic based Artificial Neural Network approach

In this article, we investigate the wave dynamics for solitons to the nonlinear bubble liquid model by applying the novel bilinear neural network approach. This equation has applications in complex fluid systems, fluid mechanics, geophysical flows, acoustic activation, and biomedical engineering. The novel bilinear neural network approach is used to obtain the exact analytical solutions for the nonlinear Bubble liquid model. These solutions are obtained in the form of single-layer and double-layer test functions, such as single-layer breather wave interaction solitons, single-layer lump wave solitons, single-layer lump waves with double exponential interactions function solutions, and double-layer rough wave interactions soliton solutions. Additionally, the Levenberg–Marquardt artificial neural network (LM-ANN) approach is used to evaluate the stability and correctness of these solutions. Fitness and regression analyses verify the accuracy and convergence of this approach, which exhibits great dependability in approximating the analytical profiles. With potential applications in complicated fluid systems and nonlinear signal processing, this work extends the study of soliton dynamics in nonlinear systems and presents a novel combination of neural network techniques with conventional soliton theory.