Solitons and peaked solitons for the general Degasperis-Procesi model
J.Noyola Rodriguez, G.Omel'yanov
TL;DR
This paper investigates a broad family of shallow water equations, establishing criteria for the existence of solitary wave solutions, including smooth solitons and peaked solitons, covering well-known models like KdV and Camassa-Holm.
Contribution
It provides new criteria for the existence of solitons and peakons within a six-parameter family of conservation laws, unifying several important shallow water models.
Findings
Criteria for soliton existence established
Conditions for peaked solitons identified
Includes models like KdV, Camassa-Holm, and Degasperis-Procesi
Abstract
We consider the general Degasperis-Procesi model of shallow water out-flows. This six parametric family of conservation laws contains, in particular, KdV, Benjamin-Bona-Mahony, Camassa-Holm, and Degasperis-Procesi equations. The main result consists of criterions which guarantee the existence of solitary wave solutions: solitons and peakons ("peaked solitons").
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Taxonomy
TopicsNonlinear Waves and Solitons · Ocean Waves and Remote Sensing · Advanced Mathematical Physics Problems