The formula for the wave profile is . Certain PDEs, like the Camassa–Holm shallow water equation, allow solutions of this form, where the peakons' positions (, ) and amplitudes (, ) depend on time in a suitable way.
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{{Information |Description=A two-peakon wave profile (solid curve) formed by superposition of two peakons (dashed curves). |Source=self-made (hand-coded SVG) |Date=2008-04-11 |Author= Hans Lundmark |Permission= |other_versions= }}