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Characteristic lines.

  For the wave equation, there are two families of characteristic lines; lines with slope dx/dt = c and lines with slope dx/dt=-c. These are shown in figure 11; the lines along which the singularities of our example propagate are shown thickened. Try following the singularities around.


  
Figure 11: Characteristic lines.
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One family of characteristics corresponds to the wave that moves to the right, and the other to the wave that moves toward the left. When the initial condition has a singularity, usually this singularity splits into a part that follows the right moving characteristic at the singularity, and a part that follows the left moving characteristic.


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