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

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

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 singul...

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Veröffentlicht in:Annales de l'Institut Henri Poincaré. Analyse non linéaire 2021-03, Vol.38 (2), p.281-300
Hauptverfasser: Linares, F., Pastor, A., Drumond Silva, J.
Format: Artikel
Sprache:eng
Schlagworte:
Dispersive blow-up
Mathematics
Mathematics, Applied
Nonlinear dispersive equations
Physical Sciences
Science & Technology
Zakharov-Kuznetsov equation
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Zusammenfassung: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.
ISSN:0294-1449
1873-1430
DOI:10.1016/j.anihpc.2020.07.002