Scattering of the 2D modified Zakharov-Kuznetsov equation

2025/06/20 by Philippe Anjolras, Anjolras, Philippe · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2506.17179

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the modified Zakharov-Kuznetsov equation in dimension 2 : ∂_t u + ∂_x ( Δu + u³ ) = 0 where u : (t, (x, y)) ∈ ℝ × ℝ² ↦ u(t, x, y) ∈ ℝ and Δ= ∂_x² + ∂_y² 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.

Cited by

• Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
• Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions

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