  We give the solution of the Whitham modulation equations for envelopes of
pulses evolving according to the sine-Gordon equation. The Whitham equations
are interpreted as the equations of relativistic hydrodynamics and their
solving is reduced by the hodograph method to solving a linear partial
differential equation. We describe the class of solutions of this equation with
separation of variables and illustrate the theory by an example of the
nonlinear wave packet evolution accompanied by its shrinking and decrease of
the number of oscillations in the Whitham nonlinear region.

Pattern Formation and Solitons