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 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.
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}
}