Let define the wave front; thus
Since in a weak wave the fields have no jump across the front, the jumps in the gradients must have the direction of and we may writeu. The square brackets denote differences between the front side and the back side of the wave.
In the field equations (10) the matrix and the productions are equal on both sides of the wave, since both only depend on and since is continuous. Thus, if we take the difference of the equations on the two sides and use (13) and (11), we obtainn – determine n wave speeds , of which the largest one is the pulse speed. Equation (15) is called the characteristic equation of the system (10) of field equations. By (11) it may be written in the form
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