Defocusing nonlinear Schrödinger equation
= Defocusing nonlinear Schrödinger equation
Writing a defocusing nonlinear Schrödinger field as $\psi=\sqrt\rho\,e^{iS}$ turns it into a continuity equation for $\rho$ and a velocity equation for $v=S_x$, including a quantum-pressure term.
In a common normalization, the defocusing case is $i\psi_t+\psi_{xx}-2|\psi|^2\psi=0$. The sign distinguishes it from the focusing <nonlinear Schrödinger equation>.