中文

Complex-valued modified Zakharov Kuznetsov equation

偏微分方程分析 2026-05-29 v1

摘要

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 T2\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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引用

@article{arxiv.2605.29265,
  title  = {Complex-valued modified Zakharov Kuznetsov equation},
  author = {Carlos E. Kenig and Nataša Pavlović and Gigliola Staffilani and Luisa Velasco},
  journal= {arXiv preprint arXiv:2605.29265},
  year   = {2026}
}