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

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.

preprint2010arXivOpen access
Ognyan ChristovSevdzhan HakkaevIliya D. Iliev
nlin.SI
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Open access3 authors1 topic
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Ognyan ChristovSevdzhan HakkaevIliya D. Iliev

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