Non-uniform continuity of periodic Holm-Staley b-family of equations


Christov O., HAKKAEV S. A., Iliev I. D.

Nonlinear Analysis, Theory, Methods and Applications, vol.75, no.13, pp.4821-4838, 2012 (SCI-Expanded, Scopus)

Abstract

We consider a family of non-evolutionary partial differential equations known as the 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 traveling waves with small amplitude. © 2012 Elsevier Ltd. All rights reserved.