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Combined soliton solutions of a (1+1)-dimensional weakly nonlocal conformable fractional nonlinear Schrödinger equation in the cubic–quintic nonlinear material

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Abstract

We concentrate on a (1+1)-dimensional weakly nonlocal conformable fractional nonlinear Schrödinger equation with cubic–quintic nonlinearities, and get some exact combined soliton solutions and periodic solutions based on the Jacobian elliptic function method and double function method. We discuss dynamical behaviors of bright soliton, dark soliton, periodic bright soliton train and periodic M-shaped soliton train, and find that shift distances along the x-direction of these solitons all add if the value of the fractional order increases.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11775185 and 11975197).

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Authors and Affiliations

  1. School of Electronics Information, Zhejiang University of Media and Communications, Hangzhou, 310018, People’s Republic of China

    Yi-Xiang Chen & Xiao Xiao

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  1. Yi-Xiang Chen
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  2. Xiao Xiao
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Correspondence to Yi-Xiang Chen.

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Chen, YX., Xiao, X. Combined soliton solutions of a (1+1)-dimensional weakly nonlocal conformable fractional nonlinear Schrödinger equation in the cubic–quintic nonlinear material. Opt Quant Electron 53, 21 (2021). https://doi.org/10.1007/s11082-020-02635-8

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