Vol. 2 No. 1 (2019)

  • Open Access

    Original Research Articles

    Article ID: 187

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

    by Georgy Omelyanov

    Insight - Physics, Vol.2, No.1, 2019; 1586 Views, 13 PDF Downloads

    DOI: https://doi.org/10.18282/ip.v2i1.187

    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.