The nonlinear Schrödinger equation (NLS) is a mathematical model used to describe the behavior of wave functions in various physical systems, particularly in quantum mechanics and optics. Unlike the linear Schrödinger equation, the NLS includes nonlinear terms, which account for interactions between waves or particles, making it suitable for phenomena like solitons and Bose-Einstein condensates. This equation is essential in understanding how waves evolve over time in media where their amplitude affects their speed and shape. Applications of the NLS extend to fields such as plasma physics, fiber optics, and fluid dynamics, where nonlinear effects play a significant role in wave propagation.