Pré-Publication, Document De Travail Année : 2025

Scattering of the 2D modified Zakharov-Kuznetsov equation

Résumé

We study the modified Zakharov-Kuznetsov equation in dimension $2$ : \[ \partial_t u + \partial_x \left( \Delta u + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \mathbb{R}^2 \mapsto u(t, x, y) \in \mathbb{R}$ and $\Delta = \partial_x^2 + \partial_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances.

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hal-05125116 , version 1 (23-06-2025)

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Philippe Anjolras. Scattering of the 2D modified Zakharov-Kuznetsov equation. 2025. ⟨hal-05125116⟩
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