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Classification Of All Travelling-wave Solutions For Some Nonlinear Dispersive Equations

Jonatan Lenells

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We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa–Holm or the Degasperis–Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles.