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.

中文翻译：

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Zakharov-Kuznetsov方程解的色散爆炸

这里的主要目的是研究Zakharov-Kuznetsov方程解的色散爆炸。色散爆炸是指由于短波或长波聚焦而引起的点奇点。我们将构造初始数据，以使线性问题的解决方案呈现出这种奇异性。然后我们证明，非线性问题的相应解存在从方程的线性分量部分继承的色散爆炸。对于广义的Zakharov-Kuznetsov方程，可以获得类似的结果。