On the mathematical theory of news waves

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.