Classification of all travelling-wave solutions for some nonlinear dispersive equations.

ABSTRACT

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.