Summary

The formula for the wave profile is ${\displaystyle u=m_{1}\exp(-|x-x_{1}|)+m_{2}\exp(-|x-x_{2}|)}$. Certain PDEs, like the Camassa–Holm shallow water equation, allow solutions ${\displaystyle u(x,t)}$ of this form, where the peakons' positions (${\displaystyle x_{1}}$, ${\displaystyle x_{2}}$) and amplitudes (${\displaystyle m_{1}}$, ${\displaystyle m_{2}}$) depend on time in a suitable way.

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