Nonlinear Dynamics

, Volume 98, Issue 3, pp 1905–1918 | Cite as

Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices

  • Z. I. DjoufackEmail author
  • F. Fotsa-Ngaffo
  • E. Tala-Tebue
  • E. Fendzi-Donfack
  • F. Kapche-Tagne
Original paper


The modulational instability associated with discrete breathers in 2D quantum ultracold atoms is studied by using the Glauber’s coherent state combined with a semi-discrete approximation and multiple-scale methods. The linear stability analysis exhibits an intriguing threshold amplitude and instability regions associated with modulational growth rate. In addition, we demonstrate a coexistence of two bright intrinsic localized modes namely, the radial symmetric and bilateral symmetric modes, at the center and at the edges of the Brillouin zone, respectively, by alternating the on-site parameter interaction. Numerical investigations reveal a good agreement with the theoretical analysis.


Discrete breathers Modulational instability Optical lattice Quantum ultracold atoms 



Z. I. Djoufack is grateful to African Institute for Mathematical Sciences (AIMS) South Africa for research facilities and computer services.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  • Z. I. Djoufack
    • 1
    • 2
    • 3
    Email author
  • F. Fotsa-Ngaffo
    • 4
    • 5
  • E. Tala-Tebue
    • 1
  • E. Fendzi-Donfack
    • 6
  • F. Kapche-Tagne
    • 1
  1. 1.Laboratoire d’Automatique et Informatique Apliquée (LAIA), Department of Telecommunication and Network EngineeringFotso Victor University Institute of TechnologyBandjounCameroon
  2. 2.Université de DschangDschangCameroon
  3. 3.African Institute for Mathematical SciencesCape TownSouth Africa
  4. 4.Institute of Wood TechnologiesUniversity of Yaounde IMbalmayoCameroon
  5. 5.Department of Physics, Faculty of ScienceUniversity of BueaBueaCameroon
  6. 6.Pure Physics Laboratory: Group of Nonlinear Physics and Complex Systems, Department of PhysicsUniversity of DoualaDoualaCameroon

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