On decay and regularity of solutions to the modified 2D Zakharov-Kuznetsov equation

This work is devoted to study the relation between regularity and decay for solutions of the two-dimensional modified Zakharov-Kuznetsov equation in the weighted Sobolev spaces $Z_{s,(r_1,r_2)}:=H^s({\mathbb{R}}^2)\cap L^2((1+\mathrm{\mid }x{\mathrm{\mid }}^{2r_1}+\mathrm{\mid }y{\mathrm{\mid }}^{2r_2})dxdy)$.