# Numerical Study of Zakharov–Kuznetsov Equations in Two Dimensions

@article{Klein2020NumericalSO, title={Numerical Study of Zakharov–Kuznetsov Equations in Two Dimensions}, author={Christian Klein and Svetlana Roudenko and Nikola M. Stoilov}, journal={Journal of Nonlinear Science}, year={2020}, volume={31} }

We present a detailed numerical study of solutions to the (generalized) Zakharov–Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document}-subcritical case, numerical evidence is presented for the stability of…

## 6 Citations

### Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov–Kuznetsov equation

- MathematicsPartial Differential Equations and Applications
- 2021

We consider the focusing modified Zakharov-Kuznetsov (mZK) equation in two space dimensions. We prove that solutions which blow up in finite time in the $H^1(\R^{2})$ norm have the property that they…

### Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations

- Mathematics, Physics
- 2022

. We present a detailed numerical study of the transverse stability of line solitons of two-dimensional, generalized Zakharov-Kusnetsov equations with various power nonlinearities. In the L 2…

### Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions

- Mathematics
- 2022

. We study stability properties of solitary wave solutions for the fractional generalized Korteweg-de equation in any spatial dimension d ≥ 1 and nonlinearity m > 1. In the L 2 -subcritical case, 1 <…

### Mock-integrability and stable solitary vortices

- Physics, MathematicsChaos, Solitons & Fractals
- 2022

### Higher dimensional generalization of the Benjamin‐Ono equation: 2D case

- MathematicsStudies in Applied Mathematics
- 2021

A higher-dimensional version of the Benjamin-Ono (HBO) equation in the 2D setting, which is L-critical, is considered, and properties of solutions both analytically and numerically are investigated, including weak and strong interactions of two solitary wave solutions.

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