Conceptually, a first order hyperbolic wave equation is the simplest wave
propagation model. The characteristic solution [20]
in the time--space
domain for the homogeneous, constant velocity model is illustrated in
Figure 2.
The first order hyperbolic system,
Equation 2, has an analytic solution, .
The initial condition is and the
slope of the characteristic solution is the media velocity **c**.

The sign of , of Equation 2 determines the propagation direction of the wave. If is positive, the wave propagates to the right. Bidirectional waves are a property of the second order hyperbolic wave equation.