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Smoothness of the solution.

  Like the convection equation, the wave equation does not smooth singularities. Figure 10 shows the evolution of a jump (with zero initial velocity of the string): the jump splits into two parts, half moving left and half moving right. There is also a jump singularity coming from the left hand boundary.


  
Figure 10: Evolution of a jump singularity.
\begin{figure} \begin{center} \leavevmode \epsffile{figures/wavjump.ps} \end{center}\end{figure}

Next: Characteristic lines. Up: The wave equation. Previous: The general solution.