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

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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 math formula.

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