Scattering problem for Zakharov-Kuznetsov equation in three space dimensions
Jun-ichi Segata
TL;DR
This paper extends the analysis of the Zakharov-Kuznetsov equation in three dimensions by constructing global solutions that scatter to free solutions without requiring small initial data, advancing understanding of its long-term behavior.
Contribution
It provides a new construction of global solutions for the 3D Zakharov-Kuznetsov equation that scatter to free solutions without smallness constraints.
Findings
Established existence of global scattering solutions in 3D
Removed smallness assumption on asymptotic states
Extended previous 2D results to three dimensions
Abstract
This paper is a continuation of our previous study arXiv:2507.01288 on the scattering problem for the Zakharov-Kuznetsov equation (ZK). When the space dimension is three, we construct a global solution to (ZK) which scatters to a given free solution without smallness assumption on the asymptotic states.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Spectral Theory in Mathematical Physics