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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.
Next: The domain and
Up: The wave equation.
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