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.

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.