Slope modulation of waves governed by sine–Gordon equation

Using the variational-asymptotic method we develop the theory of slope modulation of wave packet governed by sine–Gordon equation. A class of asymptotic solutions to the equation of slope modulation is found in terms of the density of solitons. The comparison with the exact n-soliton solution of sine–Gordon equation shows quite excellent agreement.

► The equation of slope modulation is obtained by the variational-asymptotic method.
► A class of asymptotic solutions is found in terms of the density of solitons.
► An asymptotic law for the envelop of the slope of n-soliton solution is established.
► Comparison with the exact n-soliton solution shows excellent agreement.