Hölder continuity of the solution map for the Novikov equation

Abstract

The Novikov equation (NE) has been discovered recently as a new integrable equation with cubic nonlinearities that is similar to the Camassa-Holm and Degasperis-Procesi equations, which have quadratic nonlinearities. NE is well-posed in Sobolev spaces Hs on both the line and the circle for s > 3/2, in the sense of Hadamard, and its data-to-solution map is continuous but not uniformly continuous. This work studies the continuity properties of NE further. For initial data in Hs, s > 3/2, it is shown that the solution map for NE is Hölder continuous in Hr-topology for all 0 ⩽ r < s with exponent α depending on s and r.