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Nonlocal symmetries, exact solutions, and conservation laws for the nonlinear Dirac system

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Abstract

The nonlocal symmetries of the nonlinear Dirac system are constructed on the basis of the known Lax pair. With the help of suitable auxiliary variable, the nonlocal symmetries are transformed into Lie point symmetries, while the nonlinear Dirac system is enlarged to a prolonged system that contains auxiliary variable. The soliton periodic wave interaction solution and periodic wave solution for the Dirac system are obtained using the method of similarity reduction on the prolonged system. Furthermore, the conservation laws of the Dirac system are derived.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11371326 and No.12271488).

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China

    Feng Zhang & Yi Zhang

  2. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China

    Xiangpeng Xin

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  1. Feng Zhang
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  2. Xiangpeng Xin
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  3. Yi Zhang
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Correspondence to Yi Zhang.

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Zhang, F., Xin, X. & Zhang, Y. Nonlocal symmetries, exact solutions, and conservation laws for the nonlinear Dirac system. Comp. Appl. Math. 44, 99 (2025). https://doi.org/10.1007/s40314-024-03067-w

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