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 B2,15/2(핋)2×B2,13/2(핋)2 and Bp,rs(ℝ)2×Bp,rs−1(ℝ)2(s>max{5/2,2+1/p},1≤p,r≤∞)$$ {\left({B}_{p,r}^s\left(\mathrm{\mathbb{R}}\right)\right)}^2\times {\left({B}_{p,r}^{s-1}\left(\mathrm{\mathbb{R}}\right)\right)}^2\left(s>\max \left\{5/2,2+1/p\right\},1\le p,r\le \infty \right) $$ are established by constructing new approximate solutions and initial data. [ABSTRACT FROM AUTHOR]