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In this paper, a wave-breaking criterion of strong solutions is acquired in the Soblev space H s ( S ) × H s − 1 ( S ) $H^{s}(\mathbb{S})\times H^{s-1}(\mathbb{S})$ with s > 3 2 $s>\frac{3}{2}$ by employing the localization analysis in the transport equation theory, which is different from that of the two-component Camassa-Holm system

A wave breaking criterion for a modified periodic two-component Camassa-Holm system