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Equivalence transformations and differential invariants of a generalized cubic–quintic nonlinear Schrödinger equation with variable coefficients

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Abstract

In this paper, a variable-coefficient cubic–quintic nonlinear Schrödinger equation involving five arbitrary real functions of space and time is analyzed from the point of view of symmetry analysis by using Lie’s invariance infinitesimal criterion. The infinitesimal generators of corresponding equivalence transformations are presented. The first-order differential invariants are constructed to identify when the equation can be mapped to a constant-coefficient cubic–quintic nonlinear Schrödinger equation. The constrained conditions on the variable coefficients we arrived here extend the cases discussed before and present more general results. Some brightlike and darklike solitary wave solutions for special potentials and cubic–quintic nonlinearities are obtained.

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Acknowledgements

This work was supported by the 13th Five-Year National Key Research and Development Program of China with Grant No. 2016YFC0401406 and the Fundamental Research Funds of the Central Universities with the Grant Nos. 2019MS050 and 2020MS043. The authors also thank the anonymous reviewers for helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences and Statistics, Pingdingshan University, Pingdingshan, 467000, Henan, China

    Ruijuan Li

  2. School of Mathematical Sciences and Physics, North China Electric Power University, Beijing, 102206, China

    Xuelin Yong, Yuning Chen & Yehui Huang

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Yehui Huang

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  1. Ruijuan Li
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  2. Xuelin Yong
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Correspondence to Xuelin Yong.

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Li, R., Yong, X., Chen, Y. et al. Equivalence transformations and differential invariants of a generalized cubic–quintic nonlinear Schrödinger equation with variable coefficients. Nonlinear Dyn 102, 339–348 (2020). https://doi.org/10.1007/s11071-020-05940-9

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  • DOI: https://doi.org/10.1007/s11071-020-05940-9

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