Scattering of the 2D modified Zakharov-Kuznetsov equation
Abstract
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 long times. Our proof relies on the method of space-time resonances.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Electromagnetic Scattering and Analysis
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 51
- Issue
- 0
- Pages
- 542–565
- Publication date
- 1 January 2026