Non-uniqueness for the ab-family of equations
Analysis of PDEs
2020-02-04 v1
Abstract
We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For , it is proved that there exist initial data in the Sobolev space , , with non-unique solutions. Multiple solutions are constructed by studying the collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon that for some members of the family, collision between 2-peakons can occur even if the "faster" peakon is in front of the "slower" peakon.
Keywords
Cite
@article{arxiv.2002.00399,
title = {Non-uniqueness for the ab-family of equations},
author = {John Holmes and Rajan Puri},
journal= {arXiv preprint arXiv:2002.00399},
year = {2020}
}