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Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation$u_t+u^pu_x+\alpha\mathscr{H}u_{xx}+\varepsilon u_{xyy}=0, \quad(x,y)\in\rr^2\!,\;\;t\in \rr^+\!$ in two space dimensions. Here, $\mathscr{H}$is the Hilbert transform and subscripts denote partial differentiation. Weclassify when equation (1) possesses solitary-wave solutions in terms of thesigns of the constants $\alpha$ and $\varepsilon$ appearing in the dispersiveterms and the strength of the nonlinearity. Regularity and decay properties ofthese solitary wave are determined and their stability is studied.

Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation