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

Georgy O

Abstract


We consider the general Degasperis-Procesi model of shallow wa-ter 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.


Keywords


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

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