Nonlinear Schr\"odinger Equation

The nonlinear Schrödinger equation (NLSE) describes the propagation of waves in nonlinear media, with applications ranging from fiber optics to water waves. Current research focuses on developing efficient numerical methods, particularly physics-informed neural networks (PINNs), to solve the NLSE and related inverse problems, such as identifying system parameters from observed wave behavior. These advancements improve the accuracy and efficiency of simulations, enabling better modeling of complex wave phenomena and facilitating the design of novel optical and other wave-based technologies. The interpretability of some of these new methods also offers insights into the underlying physical processes.