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Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation

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Abstract

In this article, the truncated Painlevé analysis is used to obtain the nonlocal symmetry and the Bäcklund transformation of the (1+1)-dimensional Levi equation for the first time. In addition, on these bases, the finite symmetry transformation is constructed by applying the Lie point symmetry of the prolonged system. It is proved that the (1+1)-dimensional Levi equation is solvable by consistent Riccati expansion. Then, with the help of the Riccati equation, some new exact solutions of the Levi equation are given by applying the consistent Riccati expansion method. The visual images of soliton solutions are obtained by selecting different parameters. Finally, the nonlinear self-adjointness of (1+1)-dimensional Levi equation is proved and conservation laws for the equation are constructed.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11505090), Research Award Foundation for Outstanding Young Scientists of Shandong Province (No. BS2015SF009) and the doctoral foundation of Liaocheng University under Grant No. 318051413, Liaocheng University level science and technology research fund No. 318012018.

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Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People’s Republic of China

    Yuru Hu, Feng Zhang & Xiangpeng Xin

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  1. Yuru Hu
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  2. Feng Zhang
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  3. Xiangpeng Xin
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Correspondence to Xiangpeng Xin.

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Communicated by Abdellah Hadjadj.

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Hu, Y., Zhang, F. & Xin, X. Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation. Comp. Appl. Math. 41, 219 (2022). https://doi.org/10.1007/s40314-022-01926-y

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  • DOI: https://doi.org/10.1007/s40314-022-01926-y

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