Traveling wave solutions of the Camassa–Holm equation

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Abstract

All weak traveling wave solutions of the Camassa–Holm equation are classified. We show that, in addition to smooth solutions, there are a multitude of traveling waves with singularities: peakons, cuspons, stumpons, and composite waves.

MSC

35Q35
37K45

Keywords

Water waves
Traveling waves
Camassa–Holm equation

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