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

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Abstract

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 \(\beta _1(z)\).

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Acknowledgements

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.

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  1. School of Sciences, Zhejiang A&F University, Lin’an, 311300, Zhejiang, People’s Republic of China

    Chao-Qing Dai, Yue-Yue Wang, Yan Fan & Ding-Guo Yu

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  1. Chao-Qing Dai
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  2. Yue-Yue Wang
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  3. Yan Fan
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Correspondence to Chao-Qing Dai.

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Dai, CQ., Wang, YY., Fan, Y. et al. Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under \({{\varvec{\mathcal {P}}}}{\varvec{\mathcal {T}}}\)-symmetric potentials. Nonlinear Dyn 92, 1351–1358 (2018). https://doi.org/10.1007/s11071-018-4130-4

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