Solitary Wave Solution to the Nonlinear Schrödinger Equation
This Demonstration shows the analytic solitary wave solution to the nonlinear Schrödinger's equation (NLS, or Gross–Pitaevskii equation). A solitary wave is a localized traveling wave in space. Unlike an ordinary sinusoidal wave, a solitary wave is not periodic, and is highly localized. Since the NLS is not linear, the principle of superposition does not apply and so the sum of two solitary waves is not a solution to the NLS.
The nonlinear Schrödinger equation for is , with in this Demonstration.