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The Gross-Pitaevskii Equation (GPE) is a nonlinear Schrödinger equation to take into account, still within a one-particle wavefunction, effects of particle-particle interactions, all particles being considered to be condensed into the same state. It was proposed independently by E. P. Gross[1] and L. P. Pitaevskii[2] in the context of superfluid helium and quantized vortices, both using a mean-field approach with pseudopotential interactions.
The GPE became central to describe dilute atomic gases following their experimental BEC in 1995.[3]
The Polariton Gross-Pitaevskii Equation is what interests me most.