Telegraph equation, second

A second telegraph equation [14] can be written for a magnetic field ... 

Thus, for points in the medium, where the electric and magnetic properties do not vary spatially we have obtained equations involving only the electric or magnetic fields. The two equations are of identically the same form, being the second order in partial derivatives. They are sometimes known as telegraph equations for a conductive medium. 

We call the hyperbolic system (2.17) and (2.18) a reaction-Cattaneo system. Eu and Al-Ghoul have derived such systems from generalized hydrodynamic theory [9, 7, 8, 6]. Reaction-Cattaneo systems can also be obtained from extended irreversible thermodynamics [223], see for example [282]. If we differentiate (2.17) with respect to t and (2.18) with respect to x and eliminate mixed second derivatives, we obtain the so-called reaction-telegraph equation. 

Differentiating (2.29) with respect to t and (2.30) with respect to x and eliminating the mixed second derivatives, we obtain the telegraph equation... 

During the derivation of the Fokker—Planck equation and telegrapher s equation, the derivatives with respect to distance were dropped at the second order. However, there is a case for including the third- and fourth-order spatial derivatives, though the third-order derivatives W2 will average to zero. This procedure leads to the Burnett equation... 

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