JournalsaihpcVol. 38, No. 2pp. 281–300

Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation

  • J. Drumond Silva

    Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

  • F. Linares

    IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, RJ, Brazil

  • A. Pastor

    IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas-SP, Brazil
Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation cover

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Abstract

The main purpose here is the study of dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities due to the focusing of short or long waves. We will construct initial data such that solutions of the linear problem present this kind of singularities. Then we show that the corresponding solutions of the nonlinear problem present dispersive blow-up inherited from the linear component part of the equation. Similar results are obtained for the generalized Zakharov-Kuznetsov equation.

Cite this article

J. Drumond Silva, F. Linares, A. Pastor, Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 2, pp. 281–300

DOI 10.1016/J.ANIHPC.2020.07.002