Nonlinear Schrödinger equation

The nonlinear Schrödinger equation is a mathematical model used to describe how wave-like phenomena evolve when their behavior depends not only on their current state but also on their intensity or amplitude. Unlike the standard Schrödinger equation in quantum mechanics, which is linear and describes how particles behave, the nonlinear version accounts for interactions within the wave itself, such as in optical fibers or certain fluids. It captures complex behaviors like the formation of stable localized waves called solitons, which maintain their shape over long distances due to a balance between dispersion and nonlinearity.