Nonlinear Dynamics

, Volume 92, Issue 3, pp 1261–1269 | Cite as

Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrödinger equation

  • Yue-Yue Wang
  • Chao-Qing Dai
  • Yi-Qing Xu
  • Jun Zheng
  • Yan Fan
Original Paper


A (3 + 1)-dimensional partially nonlocal nonlinear Schrödinger equation with variable coefficients is considered, and two kinds of reduction are presented. Based on these transformations, via Darboux transformation method and Hirota method, nonlocal and localized spatiotemporal soliton solutions are constructed. In the first kind of reduction, variables x and y are mixed in the single formal variable X; thus, we cannot construct completely localized structures in x and y directions. In order to discuss completely localized structures, we consider the second kind of reduction, where variables x and y are independently included in two formal variables X and Y, respectively. Based on two kinds of reduction and the related solutions, nonlocal and localized spatiotemporal soliton structures are investigated.


Nonlocal and localized spatiotemporal solitons Partially nonlocal nonlinearity (3 + 1)-Dimensional nonlinear Schrödinger equation 



This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY17A040042 and LY17F050011) and National Natural Science Foundation of China (Grant No. 11404289).


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Yue-Yue Wang
    • 1
  • Chao-Qing Dai
    • 1
  • Yi-Qing Xu
    • 1
  • Jun Zheng
    • 1
  • Yan Fan
    • 1
  1. 1.School of SciencesZhejiang A&F UniversityLin’anPeople’s Republic of China

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