In theoretical physics, the **nonlinear Schrödinger equation** (**NLS**) is a nonlinear partial differential equation. It is a classical field equation with applications to optics and water waves. Unlike the Schrödinger equation, it never describes the time evolution of a quantum state. It is an example of an integrable model.

In quantum mechanics, it is a special case of the nonlinear Schrödinger field, and when canonically quantized, it describes bosonic point particles with delta-function interactions — the particles either repel or attract when they are at the same point. The nonlinear Schrödinger equation is integrable when the particles move in one dimension of space. In the limit of infinite strength repulsion, the nonlinear Schrödinger equation bosons are equivalent to one dimensional free fermions.

Read more about Nonlinear Schrödinger Equation: Equation, Solving The Equation, Galilean Invariance, The Nonlinear Schrödinger Equation in Fiber Optics, The Nonlinear Schrödinger Equation in Water Waves, Gauge Equivalent Counterpart

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