Non‐uniform dependence on initial data of a modified periodic two‐component Camassa‐Holm system

Abstract

This paper is concerned with some properties of a modified periodic two‐component Camassa‐Holm system. By constructing two sequences of solutions of the two‐component Camassa‐Holm system, we prove that the solution map of the Cauchy problem of the two‐component Camassa‐Holm system is not uniformly continuous in .