# What are the limitations of Gross-Pitaevskij equation?

I'm a mathematician and I'm studying as an aside something about superfluids. If I understood correctly in some kind of superfluids as Bose-Einstein Condensate a wave in the fluid must satisfy the Gross-Pitaevskij equation, i.e. $$\left(-\frac{\hbar^{2}}{2m}\nabla^{2}+g\psi^{*}\psi-\mu_{0}\right)\psi=i\hbar\frac{\partial\psi}{\partial t}.$$

1. Is that right?

2. I've given to understand that this works only on BEC and at Low temperature, what are the limitations of this model?

3. Are there other more general formulas for superfluidity in general or is this one the standard to use?