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AIMS Mathematics

2025, Volume 10, Issue 3: 6318-6337. doi: 10.3934/math.2025288
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The DH5 system and the Chazy and Ramamani equations

  • 1.
    Department of Mathematics, University of Colorado, Colorado Springs, CO 80918, USA
  • 2.
    Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi, UAE
  • Published: 21 March 2025

  • MSC : 30C20, 33C05, 34A34, 34M55

  • This article considers a class of nonlinear ordinary differential equations (ODEs) whose general solutions possess a natural boundary in the complex plane and admit special solutions that are automorphic under the action of subgroups of the modular group P$ \text{SL}_2(\mathbb{Z}) $. Specifically, a $ 3 \times 3 $ matrix valued system known as the Darboux-Halphen 9 (DH9) system and its fifth-order reduction to the DH5 system are discussed. These systems arise as reductions of the self-dual Yang-Mills equations of mathematical physics. It is shown that the equations discovered by J. Chazy (1908) and V. Ramamani (1970) are embedded in the DH5 system.

    Citation: S. Chakravarty, P. Guha. The DH5 system and the Chazy and Ramamani equations[J]. AIMS Mathematics, 2025, 10(3): 6318-6337. doi: 10.3934/math.2025288

    Related Papers:

  • This article considers a class of nonlinear ordinary differential equations (ODEs) whose general solutions possess a natural boundary in the complex plane and admit special solutions that are automorphic under the action of subgroups of the modular group P$ \text{SL}_2(\mathbb{Z}) $. Specifically, a $ 3 \times 3 $ matrix valued system known as the Darboux-Halphen 9 (DH9) system and its fifth-order reduction to the DH5 system are discussed. These systems arise as reductions of the self-dual Yang-Mills equations of mathematical physics. It is shown that the equations discovered by J. Chazy (1908) and V. Ramamani (1970) are embedded in the DH5 system.



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