General solution.

  Physically, the entropy distribution, as a function of x, is simply convected toward the right with speed u. The shape of the distribution does not change. Mathematically, this can be expressed by the fact that the general solution is of the form

 

s(x,t)=s_R(x-ut),

where the shape of the function s_R still depends on the initial and boundary conditions. This represents a travelling wave.