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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Feng Zhang,
  • Xiangpeng Xin,
  • Yi Zhang

摘要

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.