Continuity properties of the data-to-solution map for the generalized Camassa–Holm equation

This work studies a generalized Camassa–Holm equation with higher order nonlinearities (g-kbCH). The Camassa–Holm, the Degasperis–Procesi and the Novikov equations are integrable members of this family of equations. g-kb  CH is well-posed in Sobolev spaces HsHs, s>3/2s>3/2, on both the line and the circle and its solution map is continuous but not uniformly continuous. In this work it is shown that the solution map is Hölder continuous in HsHs equipped with the HrHr-topology for 0⩽r