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The stability of two-dimensional spatial solitons in cubic–quintic–septimal nonlinear media with different diffractions and \({\varvec{\mathcal {PT}}}\)-symmetric potentials

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Abstract

A (2+1)-dimensional nonlinear Schrödinger equation in cubic–quintic–septimal nonlinear media with different diffractions and \({\mathcal {PT}}\)-symmetric potentials is studied, and (2+1)-dimensional spatial solitons are derived. The stable region of analytical spatial solitons is discussed by means of the eigenvalue method. The direct numerical simulation indicates that analytical spatial soliton solutions stably evolve within stable region in the media of focusing septimal and focusing or defocusing cubic nonlinearities with disappearing quintic nonlinearity under the 2D extended Scarf II potential. However, under the extended \({\mathcal {PT}}\)-symmetric potential with \(p=2\) and \(p=3\), analytical spatial soliton solutions stably evolve within stable region in the media of focusing quintic and septimal nonlinearities with defocusing cubic nonlinearity. In other cases, analytical spatial soliton solutions cannot sustain their original shapes, and they are distorted and broken up and finally decay into noise.

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Authors and Affiliations

  1. College of Engineering and Design, Zhejiang Lishui University, Lishui, 323000, Zhejiang, People’s Republic of China

    Hong-Yu Wu, Li-Hong Jiang & Yu-Feng Wu

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  1. Hong-Yu Wu
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  2. Li-Hong Jiang
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  3. Yu-Feng Wu
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Correspondence to Yu-Feng Wu.

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Wu, HY., Jiang, LH. & Wu, YF. The stability of two-dimensional spatial solitons in cubic–quintic–septimal nonlinear media with different diffractions and \({\varvec{\mathcal {PT}}}\)-symmetric potentials. Nonlinear Dyn 87, 1667–1674 (2017). https://doi.org/10.1007/s11071-016-3141-2

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  • DOI: https://doi.org/10.1007/s11071-016-3141-2

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