Mathematical analysis reveals blow-up criteria in a two-component wave equation system, indicating instability under specific initial conditions.
In this paper we investigate the two-component nonlinear dispersive wave equation on the real line. We establish a blow-up criterion for the system of coupled equations under certain natural initial profiles. The obtained criterion is only involved in the initial values u₀( x₀) u 0 x 0 and u₀( x₀) u 0 ′ x 0 at a single point x₀∈ R. x 0 ∈ R .
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Gökgöz et al. (2026) studied this question.
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