Non-smooth waves and anti-solitons in the general Degasperis-Procesi model

Georgy Omelyanov


We consider  the general Degasperis-Procesi model of shallow water out-flows, which generalizes the list of famous equations:   KdV,  Benjamin-Bona-Mahony, Camassa-Holm,  and Degasperis-Procesi.  Our main object is  the construction of non-smooth  self-similar solutions of this equation. Along with the standard waves (peakons and cuspons) we present a new type of solutions (call them "twins") which is a combination of solitons and cuspons. We demonstrate also the wave-kind dependence on the amplitude for  the waves (solitons, peakons, cuspons, and twins) with positive and negative amplitudes.


general Degasperis-Procesi model; soliton; peakon; cuspon; twins

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