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Bifurcation response and Melnikov chaos in the dynamic of a Bose–Einstein condensate loaded into a moving optical lattice

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Abstract

We investigate global bifurcation of a Bose–Einstein condensate with both repulsive two-body interaction between atoms and attractive three-body interaction loaded into a traveling optical lattice. Slow-flow equations of the traveling wave function are the first to derive and the reduced amplitude equation is obtained. The Melnikov method is applied on the reduced parametrically driven system and the Melnikov function is subsequently established. Effects of different physical parameters on the global bifurcation are studied analytically and numerically, and different chaotic regions of the parameter space are found. The results suggest that optical intensity may help to enhance chaos while the strength of the effective three-body interaction, the velocity of the optical lattice, and the damping coefficients annihilate or reduce chaotic behavior of the steady-state traveling wave solution of the particle number density of a Bose–Einstein condensate.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments. M. Siewe Siewe is indebted to the International Centre for Theoretical Physics (ICTP) for its financial support to do research work as a research visitor and also indebted to the Mathematics Group of ICTP for hosting him to undertake part of this work.

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Authors and Affiliations

  1. Faculté des sciences, Département de Physique, Laboratoire de Mécanique, Université de Yaoundé I, BP. 812, Yaoundé, Cameroon

    S. Tchatchueng, M. Siewe Siewe & C. Tchawoua

  2. Laboratory of Research on Advanced Materials and Nonlinear Science (LARAMANS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, SW-Province, Cameroon

    F. M. Moukam Kakmeni

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  1. S. Tchatchueng
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  2. M. Siewe Siewe
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Correspondence to S. Tchatchueng.

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Tchatchueng, S., Siewe Siewe, M., Moukam Kakmeni, F.M. et al. Bifurcation response and Melnikov chaos in the dynamic of a Bose–Einstein condensate loaded into a moving optical lattice. Nonlinear Dyn 75, 461–474 (2014). https://doi.org/10.1007/s11071-013-1078-2

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