Frontiers of Physics

, 15:12602 | Cite as

Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

  • Jin-Cheng Shi
  • Jian-Hua ZengEmail author
Research Article


We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one- and two-dimensional optical or matter-wave media with self-focusing nonlinearity, supported by a combination of linear and nonlinear periodic lattice potentials. The former is found to be stable once placed inside a single well of the nonlinear lattice, it is unstable otherwise. Contrary to the case with constant self-focusing nonlinearity, where the latter solution is always unstable, here, we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices. The practical possibilities for experimental realization of the predicted solutions are also discussed.


gap solitons and gap waves Bose-Einstein condensates linear and nonlinear periodic potentials 



This work was supported, in part, by the NSFC, China (Grant Nos. 61690224 and 61690222), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2016357).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.State Key Laboratory of Transient Optics and PhotonicsXi’an Institute of Optics and Precision Mechanics of CASXi’anChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic TechniqueXi’an Jiaotong UniversityXi’anChina

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