Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions

2025/07/02 by Jun‐ichi Segata, Segata, Jun-ichi · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.01288

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study long time behavior of solution to the two dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a small global solution to the Zakharov-Kuznetsov equation which scatters to a given free solution. From this result, we have the existence of wave operators for the Zakharov-Kuznetsov equation. The proof is based on the space-time resonance method developed by Gustafson-Nakanishi-Tsai and Germain-Masmoudi-Shatah etc.

Citations

• Scattering of the 2D modified Zakharov-Kuznetsov equation
• Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and\n applications
• The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation
• A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results
• Scattering theory for the Gross-Pitaevskii equation in three dimensions

Cited by

• Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation

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