Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E ] = -\frac{\partial \mathbf B}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf B] = \sigma \mathbf E + A(\mu \mathbf K + C \mathbf B ), $$ $$ \tag 3 \frac{\partial \mu}{\partial t} = D (\mathbf K \cdot \mathbf E) , \quad [\nabla \times \mathbf K] = k \mathbf K . $$ Here $A, C, D, \sigma , k$ are constant numbers, $\mathbf K$ is known.
If we can neglect term $\mu \mathbf K$ in $(2)$ and when $[\nabla \times \mathbf B] = k_{0}\mathbf B , k_{0} << k$, the solution is known. But what to do with system $(1)-(3)$ in general case? Can it be solved analytically, is there some exact solution exist?