A solution of a 3d Cartesian Poisson-Boltzmann equation

Abstract

We solve the 3d-Cartesian Poisson-Boltzmann equation (PBEq) for a 1 : 1 electric charge configuration, using the tanh, Ricatti functions and Jacobi elliptic solitary wave methods. Also, we apply a deep learning algorithm, specifically, physics-informed neural networks (PINNs), which is implemented in a Python library known as DeepXDE, finding good agreement between the analytical and the PINNs results.