TITLE:
Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction
AUTHORS:
Camus Gaston Latchio Tiofack, Thierry Blanchard Ekogo, Hermance Moussambi, Alidou Mohamadou, Timoleon C. Kofane
KEYWORDS:
Modulational Instability; Modified Gross-Pitaevskii Equation; Quantum Fluctuations
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.8,
August
1,
2012
ABSTRACT: Modulational instability conditions for the generation of localized structures in the context of matter waves in Bose-Einstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.