Non-uniqueness for the ab-family of equations

نویسندگان

چکیده

We study the cubic ab-family of equations, which includes both Fokas-Olver-Rosenau-Qiao (FORQ) and Novikov (NE) equations. For a≠0, it is proved that there exist initial data in Sobolev space Hs, s<3/2, with nonunique solutions. Multiple solutions are constructed by studying collision 2-peakon Furthermore, we prove novel phenomenon for some members family, between 2-peakons can occur even if “faster” peakon front “slower” peakon.

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2021

ISSN: ['0022-247X', '1096-0813']

DOI: https://doi.org/10.1016/j.jmaa.2020.124563