Advection-diffusion, telegraph and advection-wave equations as superpositions of transport, diffusion and wave: a didactic study

In this work we present exact solutions of the advection-diffusion and the telegraph equations. These equations are considered as combinations of the basic equations: wave, heat and transport equation. Thus, in a natural way, a third combination that we called advection-wave is introduced. Although this equation is not so popular like the other combinations, it is a simple example of didactical value that allow us to explain physical and mathematical relations for the superposition of transport and wave motion.