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Applied Math Seminar
Traveling wave solutions of the Camassa-Holm equation
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We classify all weak traveling wave solutions of the Camassa-Holm equation. It is proved that, in addition to smooth solutions, there are a multitude of traveling waves with singularities: peakons, cuspons, stumpons, and composite waves. The stability and interaction of some of these waves is investigated numerically. The approach is also shown to apply to other related nonlinear wave equations |