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This work aims to study some smoothness properties concerning the initialvalue problem associated to the dispersive generalizedBenjamin-Ono-Zakharov-Kuznetsov equation. More precisely, we prove that thesolutions to this model satisfy the so-called propagation of regularity.Roughly speaking, this principle states that if the initial data enjoys someextra smoothness prescribed on a family of half-spaces, then the regularity ispropagated with infinite speed. In this sense, we prove that regardless of thescale measuring the extra regularity in such hyperplane collection, then allthis regularity is also propagated by solutions of this model. Our analysis ismainly based on the deduction of propagation formulas relating homogeneous andnon-homogeneous derivatives in certain regions of the plane.

On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov Equation