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The classification of single traveling wave solutions for the fractional coupled nonlinear Schrödinger equation

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Abstract

The main purpose of this paper is to study the single traveling wave solutions of the fractional coupled nonlinear Schrödinger equation. By using the complete discriminant system method and computer algebra with symbolic computation, a series of new single traveling wave solutions are obtained, which include trigonometric function solutions, Jacobi elliptic function solutions, hyperbolic function solutions, solitary wave solutions and rational function solutions. As you can see, we give all the classification of single traveling wave solutions for the fractional coupled nonlinear Schrödinger equation. The obtained results substantially improve or complement the corresponding conditions in the literature (Esen and Sulaiman in Optik 167:150-156, 2018), (Eslami in Appl. Math. Comput. 258:141-148, 2016), (Han et al. in Phys. Lett. 395:127217, 2021). Finally, in order to further explain the propagation of the fractional coupled nonlinear Schrödinger equation in nonlinear optics, two-dimensional and three-dimensional graphs are drawn.

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Acknowledgements

This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20115134110001. The authors would like to thank the anonymous reviewers for their helpful suggestions and constructive comments for improving the paper.

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  1. School of Mathematical Science, Sichuan Normal University, Chengdu, 610066, People’s Republic of China

    Lu Tang & Shanpeng Chen

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  1. Lu Tang
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Correspondence to Lu Tang.

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Tang, L., Chen, S. The classification of single traveling wave solutions for the fractional coupled nonlinear Schrödinger equation. Opt Quant Electron 54, 105 (2022). https://doi.org/10.1007/s11082-021-03496-5

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