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

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

2009-12-04

arxiv.org/abs/0912.0780v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 2 figures

Scientific paper

We report wide class of exact solutions of the modified Gross-Pitaevskii equation (GPE) in `smart' Jacobi elliptic potentials: $V(\xi)=-V_{0}{\rm sn(\xi,m)}$, $V(\xi)=-V_{0}{\rm cn(\xi,m)}$, 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 fractional transform: $\rho(\xi)=\frac{A+Bf^2}{1+Df}$, where $f$ is the respective Jacobi elliptic function and the amplitude parameters $A$, $B$, and $D$ {\it nonzero}. These results generalize those contained in (Paul T, Richter K and Schlagheck P 2005 \emph{Phys. Rev. Lett.} {\bf 94}, 020404) for nonzero trapping potential.

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