Applied Mathematics

Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction

C. G. L. Tiofack, Thierry Blanchard Ekogo, Hermance Moussambi, Alidou Mohamadou, Timoléon Crépin Kofané

Published Jan 1, 2012• 2 citations

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.

DOI: 10.4236/am.2012.38125

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