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An $ ab$-family of equations with peakon traveling waves


Authors: A. Alexandrou Himonas and Dionyssios Mantzavinos
Journal: Proc. Amer. Math. Soc. 144 (2016), 3797-3811
MSC (2010): Primary 35Q53, 37K10, 37C07
DOI: https://doi.org/10.1090/proc/13011
Published electronically: February 12, 2016
MathSciNet review: 3513539
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Abstract: Peakon traveling wave solutions, both on the line and on the circle, are derived for a novel $ ab$-family of nonlocal evolution equations with cubic nonlinearities. At least two members of this $ ab$-family, namely the Fokas-Olver-Rosenau-Qiao equation and the Novikov equation, are known to be integrable. Furthermore, a generalization of the $ ab$-family with nonlinearities of order $ k\in \mathbb{N}$, $ k\geqslant 2$, is considered and its multi-peakon on the line is obtained.


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Additional Information

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: himonas.1@nd.edu

Dionyssios Mantzavinos
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: dionyssi@buffalo.edu

DOI: https://doi.org/10.1090/proc/13011
Keywords: Fokas, Olver, Rosenau, Qiao equation, Novikov equation, Camassa-Holm equation, Degasperis-Procesi equation, $b$-family of equations, integrable equations, peakon, multi-peakon, conserved quantities.
Received by editor(s): August 19, 2015
Received by editor(s) in revised form: October 24, 2015
Published electronically: February 12, 2016
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society