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<p>For the super Camassa-Holm (CH) equation proposed by Geng, Xue and Wu in 2013, a nonlocal infinitesimal symmetry quadratically depending on eigenfunctions of its linear spectral problem is constructed, and shown to be related to that of a negative flow in Geng-Wu’s super KdV hierarchy via a reciprocal transformation. It is prolonged to an enlarged system which includes the super CH equation as a subsystem. A symmetry transformation infinite form is generated for the enlarged system. Based on the finite symmetry transformation, a non-trivial exact solution, as well as a Bäcklund transformation, is constructed for the super CH equation.</p>

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On a Super Camassa-Holm Equation: Nonlocal Symmetries and Bäcklund Transformation

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Bin-fang Gao,
  • Kai Tian,
  • Zhi-han Zheng

摘要

For the super Camassa-Holm (CH) equation proposed by Geng, Xue and Wu in 2013, a nonlocal infinitesimal symmetry quadratically depending on eigenfunctions of its linear spectral problem is constructed, and shown to be related to that of a negative flow in Geng-Wu’s super KdV hierarchy via a reciprocal transformation. It is prolonged to an enlarged system which includes the super CH equation as a subsystem. A symmetry transformation infinite form is generated for the enlarged system. Based on the finite symmetry transformation, a non-trivial exact solution, as well as a Bäcklund transformation, is constructed for the super CH equation.