Need help solving Darboux equation

[xdrgnh]

I'm working on a personal math project and I'm running into this system of differential equations.

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

 

[jedishrfu]

I’m guessing this is differential geometry so I found this reference to a darboux frame

https://en.m.wikipedia.org/wiki/Darboux_frame