Abstract
We investigate the blow-up phenomena for the two-component generalizations of nonlinear dispersive wave equation on the real line that includes the two-component Camassa-Holm system as well as the system for the hyperelastic-rod wave equation as special cases. We establish a blow-up criterion for system of coupled equations under certain natural initial profiles. The obtained criterion involves only the properties of the data u0 in a neighbourhood of a single point and consequently, it is local-in-space with respect to first component of the system under consideration.
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