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arXiv · 2605.29265

Complex-valued modified Zakharov Kuznetsov equation

Carlos E. Kenig·Nataša Pavlović·Gigliola Staffilani·Luisa Velasco
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Abstract

Motivated by the introduction of the Zakharov-Kuznetsov equation as a higher dimensional generalization of the Korteweg-de Vries equation, in this paper we introduce the modified Zakharov-Kuznetsov (mZK) equation as a 2-dimensional generalization of the complex-valued modified Korteweg-de Vries equation. We initiate the mathematical analysis of the mZK equation on $\mathbb{T}^2$ by proving a local well-posedness result in Sobolev spaces and by establishing a failure of uniform continuity. We also note that the real-valued version of the mZK equation has physical significance.

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Carlos E. Kenig, Nataša Pavlović, Gigliola Staffilani, Luisa Velasco. 2026-05-28. Complex-valued modified Zakharov Kuznetsov equation. https://arxiv.org/abs/2605.29265

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