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G. Theocharis, Z. Rapti, P. G. Kevrekidis, D. J. Frantzeskakis and V. V. Konotop, “Modulational Instability of Gross-Pitaevskii-Type Equations in 1+1 Dimensions,” Physics Review A, Vol. 67, No. 6, 2003, Article ID: 063610. doi:10.1103/PhysRevA.67.063610

has been cited by the following article:

• 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.