On the Cauchy problem for a four-component Novikov system with peaked solutions

Considered herein is the Cauchy problem for a four-component Novikov system with peaked solutions. We first investigate the local Gevrey regularity and analyticity of the solutions by a generalized Ovsyannikov theorem. Then, based on the local well-posedness of this problem, the results with respect to the nonuniformly continuous dependence on initial data of the solutions in Besov spaces ( B-5/2 (2,1) (T))(2) X (B-3/2 (2,1) (T))(2 )and (B-p,r(s)(R))(2) X (B- p,r (s-1)(R))(2)(s > max{5/2, 2+1/p}, 1 = p, r = 8) are established by constructing new approximate solutions and initial data.