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How can i find the wave equation for B-field for non-zero charge density(rho) and non-zero current density J?

  1. Take the curl of (curl of B)
  2. curl of RHS of the Ampere-Maxwell law gives curl of J and second degree partial timederivative of the B.

my problem is: what is the curl of J?

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The curl of $J$ is your source for new undulations in the field. It doesn't “go away” if that’s what you are wondering: though one can indirectly make it go away by instead looking for an equation for the vector potential, at which point you can take the Lorenz gauge to get rid of $\rho$ so that you simply get $$c^{-2}\ddot A - \nabla^2 A= \mu_0 J.$$

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