Physics-informed neural network solution of the generalized (1+1) dimensional Sine-Gordon equation

We employed a novel physics-informed neural networks (PINN) to tackle (1+1) dimensional Sine-Gordon equation (SGE). A test problem with known analytical solution is numerically solved to demonstrate the effectiveness of the PINN, and compared to standard explicit finite difference method (EFDM) and Chen-Charpentier et al.’s finite difference method (CCFDM). Although the three methods used show good agreement, our research shows that the EFDM results accord with the analytical solution the best. Given the consistent agreement between the numerical results obtained by all three methods and the analytical solution, all three methods are recommended as competitive options. The methods employed in this study can be a valuable asset for present and future model developers engaged in various nonlinear physical wave phenomena, such as solitons evolution or soliton interaction as well as optical pulses propagation in nonlinear media, including optical fibers.