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Effective dynamics for $N$-solitons of the Gross-Pitaevskii equation
Effective dynamics $N$-solitons Gross-Pitaevskii equation
2010/12/13
We consider several solitons moving in a slowly varying external eld. We show that the e ective dynamics obtained by restricting the full Hamiltonian to the nite dimensional manifold of N-solitons (...
Exact solutions of the modified Gross-Pitaevskii equation in `smart' periodic potentials in the presence of external source
exact solutions modified Gross-Pitaevskii equation
2010/4/6
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(\x...
Numerical Solution of the Two-Dimensional Gross-Pitaevskii Equation for Trapped Interacting Atoms
Numerical Solution Two-Dimensional Gross-Pitaevskii Equation Trapped Interacting Atoms
2010/10/18
We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zer...
Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain
Semiclassical Limit Gross-Pitaevskii Equation Exterior Domain
2018/4/20
In this paper, we study the semiclassical limit of the Gross-Pitaevskii equation (a cubic nonlinear Schrodinger quation) with the Neumann boundary condition in an exterior domain. We prove that befor...
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
Similarity Solutions and Collapse Attractive Gross-Pitaevskii Equation
2010/11/2
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling con...