An 𝑎𝑏-family of equations with peakon traveling waves

Himonas, A.; Mantzavinos, Dionyssios

doi:10.1090/proc/13011

An $ab$-family of equations with peakon traveling waves
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by A. Alexandrou Himonas and Dionyssios Mantzavinos PDF

Proc. Amer. Math. Soc. 144 (2016), 3797-3811 Request permission

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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