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An Analysis of the Lie Symmetry and Conservation Law of a Variable-Coefficient Generalized Calogero–Bogoyavlenskii–Schiff Equation in Nonlinear Optics and Plasma Physics

Author

Listed:
  • Shu Miao

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Zi-Yi Yin

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Zi-Rui Li

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Chen-Yang Pan

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Guang-Mei Wei

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

Abstract

In this paper, the symmetries and conservation laws of a variable-coefficient generalized Calogero–Bogoyavlenskii–Schiff (vcGCBS) equation are investigated by modeling the propagation of long waves in nonlinear optics, fluid dynamics, and plasma physics. A Painlevé analysis is applied using the Kruskal-simplified form of the Weiss–Tabor–Carnevale (WTC) method, which shows that the vcGCBS equation does not possess the Painlevé property. Under the compatibility condition ( a 1 ( t ) = a 2 ( t ) ), infinitesimal generators and a symmetry analysis are presented via the symbolic computation program designed. With the Lagrangian, the adjoint equation is analyzed, and the vcGCBS equation is shown to possess nonlinear self-adjointness. Based on its nonlinear self-adjointness, conservation laws for the vcGCBS equation are derived by means of Ibragimov’s conservation theorem for each Lie symmetry.

Suggested Citation

  • Shu Miao & Zi-Yi Yin & Zi-Rui Li & Chen-Yang Pan & Guang-Mei Wei, 2024. "An Analysis of the Lie Symmetry and Conservation Law of a Variable-Coefficient Generalized Calogero–Bogoyavlenskii–Schiff Equation in Nonlinear Optics and Plasma Physics," Mathematics, MDPI, vol. 12(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3619-:d:1524906
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