In a coupled phase oscillator problem, one often encounters adler's equation which for two oscillators is given by:
$\frac{d\phi}{dt} = \Delta\omega - Ksin(\phi)$
where $\phi$ is the phase difference between oscillators. $\Delta\omega, K$ are constants.
Now this equation can be solved analytically. However, I have a system of three coupled oscillators for which the corresponding adler equations are:
$$ \begin{cases} \frac{d\phi_1}{dt} = \Delta\omega_1 - K_1\sin(\phi_1) - K_2\sin(\phi_2)\\ \frac{d\phi_2}{dt} = \Delta\omega_2 - K_3\sin(\phi_1) - K_4\sin(\phi_2) \end{cases} $$ where, $K_1,K_2,K_3,K_4,\Delta\omega_1, \Delta\omega_2$ are all constants.
Can these coupled equations be solved analytically ?
It would be helpful even if it can be done with some approximations!