Soliton Solution

Soliton solutions represent stable, self-reinforcing waves that maintain their shape and speed during propagation, a phenomenon studied across diverse fields. Current research focuses on leveraging deep learning, particularly physics-informed neural networks (PINNs) and Fourier neural operators (FNOs), to model and discover soliton dynamics in various nonlinear systems, including the Schrödinger and Korteweg-de Vries equations. This work addresses both forward problems (predicting soliton behavior) and inverse problems (identifying system parameters from observed solutions). These advancements have implications for understanding complex wave phenomena in diverse areas like nonlinear optics, fluid dynamics, and even social dynamics (e.g., modeling information spread).