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Non-local symmetries, exact solutions and conservation laws for the coupled Lakshmanan–Porsezian–Daniel equations

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Abstract

The non-local symmetries of the coupled Lakshmanan–Porsezian–Daniel (LPD) equations are obtained with the help of the known Lax pair. By introducing an auxiliary variable, the coupled LPD equations are extended to a closed prolonged system and the non-local symmetries are localised to the Lie point symmetries of the prolonged system. Furthermore, based on the Lie point symmetries of the prolonged system, the exact solutions and non-local conservation laws of the coupled LPD equations are derived.

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Acknowledgements

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

    Feng Zhang, Yuru Hu, Xiangpeng Xin & Hanze Liu

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

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Zhang, F., Hu, Y., Xin, X. et al. Non-local symmetries, exact solutions and conservation laws for the coupled Lakshmanan–Porsezian–Daniel equations. Pramana - J Phys 96, 199 (2022). https://doi.org/10.1007/s12043-022-02436-6

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  • DOI: https://doi.org/10.1007/s12043-022-02436-6

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