Continuity properties of the solution map for the four-component Novikov system with peakon solutions

Abstract

Considered herein is the Cauchy problem for the four-component Novikov system with peakon solutions on the line. At first, we establish the result with respect to the non-uniform continuity of the solution map of this problem in the critical Besov spaces (B2,13/2(R))2×(B2,15/2(R))2. Then, the Hölder continuity of the solution map in Sobolev spaces is discussed.