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February 26, 2026Monatshefte für Mathematik0 citationsOpen Access

Blow-up criteria for some two-component shallow water wave system

PGPelin Ayşe GökgözENEmil NovruzovGebze Technical University

Key Points

  • To establish a blow-up criterion for a system of coupled nonlinear dispersive wave equations based on initial profiles.
  • Investigated a two-component nonlinear dispersive wave equation on the real line.
  • Analyzed the system's behavior concerning natural initial profiles.
  • Developed criteria dependent on initial values at specific points.
  • Identified conditions under which blow-up occurs in the wave system.
  • Demonstrated that initial values influence the system's stability.
  • Provided a mathematical foundation for future studies on wave behavior.

Abstract

Abstract 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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Cite This Study

Gökgöz et al. (2026) studied this question.

synapsesocial.com/papers/699fe39d95ddcd3a253e7a66https://doi.org/10.1007/s00605-026-02164-8
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