Scattering of the 2D modified Zakharov-Kuznetsov equation

We study the modified Zakharov-Kuznetsov equation in dimension $2$ : $${\mathrm{\partial }}_{t}u+{\mathrm{\partial }}_x(\mathrm{\Delta }u+u^3)=0$$ where $u:(t,(x,y))\in \mathbb{R}\times {\mathbb{R}}^2\mapsto u(t,x,y)\in \mathbb{R}$ and $\mathrm{\Delta }={\mathrm{\partial }}_x^2+{\mathrm{\partial }}_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances.