Abstract
Peakon traveling wave solutions on the circle are derived for the cubic -family of equations, which includes both the Fokas–Olver–Rosenau–Qiao (FORQ) and Novikov (NE) equations. For , it is proved that there exists an initial data in the Sobolev space , , with nonunique solutions on the circle. We construct a two-peakon solution with an asymmetric peakon–antipeakon initial profile that collides at a finite time. At the time of collision, the two-peakon solution reduces to a single peakon solution, which will complete the proof of nonuniqueness.
Citation
Rajan Puri. "Nonuniqueness for the -family of equations with peakon travelling waves on the circle." Rocky Mountain J. Math. 52 (2) 707 - 715, April 2022. https://doi.org/10.1216/rmj.2022.52.707
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