  The paper presents the solutions for the two-beam reduction of the dense
soliton gas equations (or Born-Infeld equation) obtained by analytical and
numerical methods. The method proposed by the authors is used. This method
allows to reduce the Cauchy problem for two hyperbolic quasilinear PDEs to the
Cauchy problem for ODEs. In some respect, this method is analogous to the
method of characteristics for two hyperbolic equations. The method is
effectively applicable in all cases when the explicit expression for the
Riemann-Green function for some linear second order PDE, resulting from the use
of the hodograph method for the original equations, is known. The numerical
results for the two-beam reduction of the dense soliton gas equations, and the
shallow water equations (omitting in the previous papers) are presented. For
computing we use the different initial data (periodic, wave packet).
