Need help solving Darboux equation

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SUMMARY

The discussion centers on solving the Darboux equation, specifically a system of nonlinear ordinary differential equations (ODEs). The user seeks resources in English regarding Hermite modular elliptic functions, which are essential for finding solutions to the equation. They express difficulty due to the lack of accessible references and their unfamiliarity with the mathematical concepts involved. The mention of the Darboux frame indicates a connection to differential geometry, which is relevant to their project.

PREREQUISITES
  • Understanding of nonlinear ordinary differential equations (ODEs)
  • Familiarity with differential geometry concepts
  • Knowledge of Hermite modular elliptic functions
  • Ability to navigate mathematical literature in English
NEXT STEPS
  • Research Hermite modular elliptic functions and their applications
  • Study the properties and applications of the Darboux frame in differential geometry
  • Explore resources on solving nonlinear ordinary differential equations
  • Look for English translations or summaries of French literature on the Darboux equation
USEFUL FOR

Mathematicians, students in differential geometry, and anyone tackling complex systems of nonlinear ordinary differential equations.

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I'm working on a personal math project and I'm running into this system of differential equations.
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I have seen references which state the solutions are in terms of Hermite modular elliptic functions, but I do not know what those functions are. All of the references I can find on this equation are in french and I do not read french at all. Can anyone point me to any material in English or provide any suggestion of how to tackle this system of nonlinear ode's? I'm doing a project in geometry and did not expect to get these complicated ODE's that I never seen before and have solutions in terms of functions I never heard of.

Thanks
 

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