# On the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation

## TL;DR

This paper reviews recent results on the unique continuation property of solutions to the 2D Zakharov-Kuznetsov equation and provides an alternative, more adaptable proof that could extend to higher dimensions.

## Contribution

It offers a new proof of the optimal unique continuation property that is less sensitive to the problem's dimensionality, enabling potential extension to higher-dimensional cases.

## Key findings

- Confirmed the optimal unique continuation property for 2D solutions
- Developed an alternative proof strategy adaptable to higher dimensions
- Enhanced understanding of Zakharov-Kuznetsov equation's solution behavior

## Abstract

The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the other hand, the main core of the work is devoted to providing an alternative proof of the aforementioned result. The importance of this original contribution relies on the fact that, unlike the approach used in [4], the strategy adopted here is not sensitive of the two dimensional setting of the problem and therefore could be adapted to higher dimensional Zakharov-Kuznetsov equations for which, as far as we know, a proof of an analogous optimal unique continuation principle is still missing. For sake of clearness we focus here on the 2D case only, the higher dimensional analysis will be discussed somewhere else.