Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: SLMath: Opening Doors to Mathematics, Collaborative Research: On New Directions for the Derivation of Wave Kinetic Equations, G4713160749, FRG: Collaborative Research: New Challenges in the Derivation and Dynamics of Quantum Systems, Harmonic Analysis and Partial Differential Equations, FRG: Collaborative Research: New Challenges in the Derivation and Dynamics of Quantum Systems, G5575423, RTG: Analysis of Partial Differential Equations, G5723837661, G8896166621, Large Systems of Interacting Particles and Waves and Their Effective Equations
OpenAlex ID: W7162802291
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