Oscillatory instabilities of gap solitons in a repulsive Bose-Einstein condensate

PHYSICA D-NONLINEAR PHENOMENA

卷:337

Article

Kizin, P. P.¹  Zezyulin, D. A.^2,3  Alfimov, G. L.¹ 

[1] Natl Res Univ Elect Technol MIET, Moscow 124498, Russia

[2] Univ Lisbon, Fac Ciencias, Ctr Fis Teor & Computat, Campo Grande,Ed C8, P-1749016 Lisbon, Portugal

[3] Univ Lisbon, Fac Ciencias, Dept Fis, Campo Grande,Ed C8, P-1749016 Lisbon, Portugal

关键词: Gross-Pitaevskii equation;    Optical lattice;    Gap solitons;    Stability;    Evans function;   

DOI  :  10.1016/j.physd.2016.07.007

来源: Elsevier

【 摘 要 】

The paper is devoted to numerical study of stability of nonlinear localized modes (gap solitons) for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with periodic potential and repulsive interparticle interactions. We use the Evans function approach combined with the exterior algebra formulation in order to detect and describe weak oscillatory instabilities. We show that the simplest (fundamental) gap solitons in the first and in the second spectral gap undergo oscillatory instabilities for certain values of the frequency parameter (i.e., the chemical potential). The number of unstable eigenvalues and the associated instability rates are described. Several stable and unstable more complex (non-fundamental) gap solitons are also discussed. The results obtained from the Evans function approach are independently confirmed using the direct numerical integration of the GPE. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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