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We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons,which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficientlystrong, from the strong-coupling limit of the Bogoliubov–de Gennes equations that describe superfluidfermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskiiequation are also obtained by our approach. Our results are relevant to the recent advances withultracold fermionic atoms in a trap

Derivation of the Gross-Pitaevskii Equation for Condensed Bosons from the Bogoliubov–de Gennes Equations for Superfluid Fermions