Nonlinear Dynamics

, Volume 92, Issue 3, pp 1351–1358 | Cite as

Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under \({{\varvec{\mathcal {P}}}}{\varvec{\mathcal {T}}}\)-symmetric potentials

  • Chao-Qing Dai
  • Yue-Yue Wang
  • Yan Fan
  • Ding-Guo Yu
Original Paper


Gaussian spatial soliton solutions of both the constant-coefficient and variable-coefficient (2 + 1)-dimensional nonlinear Schrödinger equations in quintic–septimal nonlinear materials with different diffractions are presented under two kinds of \({\mathcal {P}}{\mathcal {T}}\)-symmetric potentials. The linear stability analysis and direct numerical simulation are jointly utilized to investigate the stability for analytical solutions of the constant-coefficient equation. Results from the linear stability analysis and the direct numerical simulation possess a high degree of consistency, that is, the stable case for Gaussian spatial solitons of the constant-coefficient equation appears only in the defocusing quintic and focusing septimal nonlinear material. Moreover, reconstruction of stable Gaussian spatial solitons of the variable-coefficient equation is studied based on the expression of the effective propagation distance Z(z) by choosing an appropriate form of diffraction \(\beta _1(z)\).


Gaussian spatial solitons Reconstruction of stability Quintic–septimal nonlinearities \({\mathcal {P}}{\mathcal {T}}\)-symmetric potential 



This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F050011) and the National Natural Science Foundation of China (Grant No. 11375007). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China, Open Fund of IPOC (BUPT) and Youth Top-notch Talent Development and Training Program of Zhejiang A&F University.

Compliance with ethical standards

Conflict of interest

The authors have declared that no conflict of interest exists.


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Copyright information

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

Authors and Affiliations

  • Chao-Qing Dai
    • 1
  • Yue-Yue Wang
    • 1
  • Yan Fan
    • 1
  • Ding-Guo Yu
    • 1
  1. 1.School of SciencesZhejiang A&F UniversityLin’anPeople’s Republic of China

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