TY  - JOUR
AU  - Chakravarty, S.
AU  - Guha, P.
PY  - 2025
TI  - The DH5 system and the Chazy and Ramamani equations
JO  - AIMS Mathematics
SP  - 6318
EP  - 6337
VL  - 10
IS  - 3
AB  - 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       SL    2    (      Z    ). Specifically, a    3  ×  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.
UR  - https://doi.org/10.3934/math.2025288
DO  - 10.3934/math.2025288