Non-uniform continuity of periodic Holm-Staley \(b\)-family of equations

DOI10.1016/J.NA.2012.03.031zbMATH Open1251.35123arXiv1010.3807OpenAlexW1996417512MaRDI QIDQ435052

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Publication date: 16 July 2012

Published in: (Search for Journal in Brave)

Abstract: We consider a family of non-evolutionary partial differential equations known as Holm - Staley b - family which includes the integrable Camassa-Holm and Degasperis-Procesi equations. We show that the solution map is not uniformly continuous. The proof relies on a construction of smooth periodic travelling waves with small amplitude.

Full work available at URL: https://arxiv.org/abs/1010.3807

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