The Propagation of Disturbances in Dispersive Media

Cover The Propagation of Disturbances in Dispersive Media
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It is unnecessary to work through the details of the exact solution of (130) under the initial conditions given in (133) ; the equation is similar to one which has been studied in connection with damped electric vibrations, known as the telegraphists' equation, and in fact only differs from it by the coefficient of z in the last term being positive instead of negative.
An exact solution can be obtained in the form Jx-t p + ir*Mp)F{q)dq, Jx—t where P^ Jif'-ix-qf} ^ (134).
In particular, put f{x)
... = 0, and F{x) = tt/c in the range - € a; (135). .
We can compare this solution with the approximate evaluation by group methods applied to a Fourier integral. Before doing so, it is of interest to obtain it in any other way by using a Fourier integral with complex variable.


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