April 2022 Nonuniqueness for the ab-family of equations with peakon travelling waves on the circle
Rajan Puri
Rocky Mountain J. Math. 52(2): 707-715 (April 2022). DOI: 10.1216/rmj.2022.52.707

Abstract

Peakon traveling wave solutions on the circle are derived for the cubic ab-family of equations, which includes both the Fokas–Olver–Rosenau–Qiao (FORQ) and Novikov (NE) equations. For a0, it is proved that there exists an initial data in the Sobolev space Hs, s<32, 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

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Rajan Puri. "Nonuniqueness for the ab-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

Information

Received: 5 April 2021; Revised: 9 July 2021; Accepted: 10 July 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

MathSciNet: MR4422961
zbMATH: 1492.35231
Digital Object Identifier: 10.1216/rmj.2022.52.707

Subjects:
Primary: 35Q35

Keywords: Camassa–Holm equation , Cauchy problem , Initial value problem , peakon , Sobolev Spaces , solitons , well-posedness

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.52 • No. 2 • April 2022
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