Nonlinear Schrodinger Equation

The nonlinear Schrödinger equation (NLSE) is a mathematical model that describes how certain wave-like phenomena, such as light in optical fibers or waves in special materials, change and interact when their behavior depends on their own intensity or amplitude. Unlike linear equations where waves don't affect each other, the NLSE accounts for nonlinear effects—meaning the wave's properties influence its evolution, leading to complex behaviors like solitons (stable wave packets). It is fundamental in understanding systems where wave interactions are significant, capturing both the wave's propagation and nonlinear interactions within the same framework.