Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 144, Issue 9, Pages 3797-3811Publisher
AMER MATHEMATICAL SOC
DOI: 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
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Funding
- Simons Foundation [246116]
- AMS-Simons Travel Grant
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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 is an element of N, k >= 2, is considered and its multi-peakon on the line is obtained.
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