  We establish well-posedness conclusions for the Cauchy problem associated to
the dispersion generalized Zakharov-Kutnesov equation in bi-periodic Sobolev
spaces $H^{s}\left(\mathbb{T}^{2}\right)$,
$s>(\frac{3}{2}-\frac{1}{2^{\alpha+2}})(\frac{3}{2}-\frac{\beta}{4})$.
