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

Georgy Omelyanov

doi:10.18282/ip.v2i1.187

Georgy Omelyanov University of Sonora

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

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

Abstract

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.

Author Biography

Georgy Omelyanov, University of Sonora

Prof. GEORGY OMELYANOV was born October 3, 1950 in Moscow, USSR.

He received his Master Level in 1973 and he was awarded a PhD in Differential Equations in 1981 both at Moscow State Institute of Electronics and Mathematics. In 1993, he was awarded a “Full Doctor” degree at Moscow State Lomonosov University.

He was an Associated Professor, Professor and Full Professor at Moscow State Institute of Electronics and Mathematics from 1973 – 2002. Since 2002 he is a Full Professor at the Mathematical Department of University of Sonora, Mexico.

He has published 3 monographs and more than 80 scientific articles. The total number of citations exceeds 600.

He is a member of the “Sistema Nacional de Investigadores”, Mexico, level 3, of the Mexican Academy of Sciences, and the Editorial Board of “Journal T-Comm”.

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