An $ab$-family of equations with peakon traveling waves
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- by A. Alexandrou Himonas and Dionyssios Mantzavinos PDF
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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.References
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Additional Information
- A. Alexandrou Himonas
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 86060
- Email: himonas.1@nd.edu
- Dionyssios Mantzavinos
- Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
- MR Author ID: 925372
- Email: dionyssi@buffalo.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3797-3811
- MSC (2010): Primary 35Q53, 37K10, 37C07
- DOI: https://doi.org/10.1090/proc/13011
- MathSciNet review: 3513539