Undergrad Configuring Laws of Motion: Static/Dynamic

[Maniac_XOX]

TL;DR

Is it possible to derive equations for electric field E and magnetic B from the following equation?

$$\Box A_\alpha +\mu^2 A_\alpha = 2\beta A_\mu \partial_\alpha A^\mu + \frac {4\pi}{c} J_\alpha$$

where $A=(\Phi, \vec A)$ and $J=(\rho, \vec J)$

using a static configuration first where $α=0$
and then a dynamic one where $α=i$

knowing that $E= - \nabla^2 \Phi - \frac {\partial A}{dt}$ and $B= \nabla \times A$ and $-\nabla^2 A + \nabla (\nabla A) = \nabla \times (\nabla \times A)$

I personally tried but because of the $2\beta A_\mu$ term i cannot connect these

My attempts so far:
For static configuration $$- \frac {\partial \Phi}{c^2 \partial t^2} + \nabla^2 \Phi +\mu^2 \Phi = 2\beta A_\mu \frac {\partial A^\mu}{\partial t} + \frac {4\pi}{c} \rho$$
For dynamic configuration $$- \frac {\partial \vec A}{c^2 \partial t^2} + \nabla^2 \vec A +\mu^2 \vec A = 2\beta A_\mu \nabla \vec A + \frac {4\pi}{c} \vec J$$

 

[Maniac_XOX]

[CORRECTION] $E=-\nabla \Phi- \frac {\partial A}{\partial t}$
For static configuration $$\nabla^2 \Phi +\mu^2 \Phi = + \frac {4\pi}{c} \rho$$
since in static configuration $\frac {\partial}{\partial t}=0$

can someone help me derive Maxwell's equations for these equations if it's possible?