A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross-Pitaevskii equation - Hendy, Ahmed S.; Macías-Díaz, Jorge E. (Zielona Góra: Uniwersytet Zielonogórski)
The present work departs from an extended form of the classical multi-dimensional Gross-Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified.
Keywords: generalized Gross-Pitaevskii system; Riesz fractional diffusion; discrete uniform Sobolev inequality; conservative method; optimal error bounds