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We report wide class of exact solutions of the modified Gross-Pitaevskiiequation (GPE) in `smart' Jacobi elliptic potentials: $V(\xi)=-V_{0}{\rmsn(\xi,m)}$, $V(\xi)=-V_{0}{\rm cn(\xi,m)}$, and $V(\xi)=-V_{0}{\rm dn(\xi,m)}$in the presence of external source. Solitonlike solutions, singular solutions,and periodic solutions are found using a recently developed fractionaltransform: $\rho(\xi)=\frac{A+Bf^2}{1+Df}$, where $f$ is the respective Jacobielliptic function and the amplitude parameters $A$, $B$, and $D$ {\it nonzero}.These results generalize those contained in (Paul T, Richter K and Schlagheck P2005 \emph{Phys. Rev. Lett.} {\bf 94}, 020404) for nonzero trapping potential.

Exact solutions of the modified Gross-Pitaevskii equation in `smart' periodic potentials in the presence of external source