1
$\begingroup$

I'm looking for a Bäcklund transformation linking the following two nonlinear differential equations for real $t$: $$\dfrac{d^2}{dt^2}f(t)=\cos\left[f(t)\right]$$ $$\dfrac{d^2}{dt^2}g(t)=\sinh\left[g(t)\right]$$ where $f$, $g$ are real-valued $C^2$ functions. How can I find it? Thanks

$\endgroup$
  • $\begingroup$ @LoïcTeyssier: Sorry. I corrected the typos $\endgroup$ – Riccardo.Alestra Jul 8 '14 at 11:52
1
$\begingroup$

To relate the solutions of these equations, the following simple transformation can be employed: $$g= i \left(\frac\pi2-f\right),$$ where $i$ stands for the imaginary unit, but I don't see any simple way for finding a transformation that would send real solutions of one equations into real solutions of the other.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.