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

Discrete and Continuous Dynamical Systems 2026 Open access

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Authors: Jun-ichi Segata
DOI: 10.3934/dcds.2026029
Cited by: 2
References: 28

Abstract

In this paper, we study the long-time behavior of solutions to the two-dimensional Zakharov-Kuznetsov equation in the framework of the final-state problem. We construct a small global solution that scatters to a given free solution. From this result, we obtain the existence of wave operators for the Zakharov-Kuznetsov equation. The proof is based on the space-time resonance method developed by Gustafson, Nakanishi, and Tsai (Commun. Contemp. Math. 11 (2009), 657-707) and by Germain, Masmoudi, and Shatah (Int. Math. Res. Not. (2009), 414-432; J. Math. Pures Appl. (9) 97 (2012), 505-543).

Fields of Study & Subjects

Advanced Mathematical Physics Problems Nonlinear Waves and Solitons Stability and Controllability of Differential Equations

Publication details

Journal / source
Discrete and Continuous Dynamical Systems
Publisher
American Institute of Mathematical Sciences (AIMS)
Volume
51
Issue
0
Pages
230–249
Publication date
1 January 2026