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Wave Equation

Describes the propagation of electromagnetic waves, relating the change in the electric and magnetic fields over space and time: \nabla imes \vec{E} = - \frac{\partial \vec{B}}}{\partial t}.”
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The statement of the theorem

In the vacuum (ρ=0,J⃗=0\rho=0, \vec{J}=0), the propagation of the electric field E⃗(r⃗,t)\vec{E}(\vec{r}, t) and the magnetic field B⃗(r⃗,t)\vec{B}(\vec{r}, t) is governed by the homogeneous Maxwell's equations. The resulting wave equation for both fields is given by the d'Alembertian operator □2\Box^2: \n\n□2E⃗=(∇2−1c2∂2∂t2)E⃗=0\Box^2 \vec{E} = \left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \vec{E} = 0 \n\n□2B⃗=(∇2−1c2∂2∂t2)B⃗=0\Box^2 \vec{B} = \left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \vec{B} = 0 \n\nWhere c=1/ϵ0μ0c = 1/\sqrt{\epsilon_0 \mu_0} is the speed of light in vacuum, and ∇2\nabla^2 is the Laplacian operator. These equations imply that the fields satisfy the general form of a hyperbolic partial differential equation, characterizing wave propagation in a source-free medium.
Source: Wikipedia