  We discuss the spread of a piece of news in a population. This is modeled by
SIR model of epidemic spread. The model can be reduced to a nonlinear
differential equation for the number of people affected by the news of
interest. The differential equation has an exponential nonlinearity and it can
be approximated by a sequence of nonlinear differential equations with
polynomial nonlinearities. Exact solutions to these equations can be obtained
by the Simple Equations Method (SEsM). Some of these exact solutions can be
used to model a class of waves associated with the spread of the news in a
population. The presence of exact solutions allow to study in detail the
dependence of the amplitude and the time horizon of the news waves on the wave
parameters such as the size of the population, initial number of spreaders of
the piece of the news, transmission rate and recovery rate. This allows for
recommendations about the change of wave parameters in order to achieve a large
amplitude or appropriate time horizon of the news wave. We discuss 5 types of
news waves on the basis of the values of the transmission rate and recovery
rate - the types A,B,C,D and E of news waves. In addition, we discuss the
possibility of building wavetrains by news waves. There are three possible
kinds of wavetrains with respect of the amplitude of the wave: increasing
wavetrain, decreasing wavetrain, and mixed wavetrain. The increasing wavetrain
is especially interesting as it is connected to an increasing amplitude of the
news wave with respect to the amplitude of the previous wave of the wavetrain.
It can find applications in advertising, propaganda, etc.
