Qualitative properties of solutions of an integral equation associated with the Benjamin-Ono-Zakharov-Kuznetsov operator

We study qualitative properties of solutions of an integral equation associated the Benjamin-Ono-Zakharov-Kuznetsov operator. We establish the regularity of the positive solutions without the assumption of being in fractional Sobolev-Liouville spaces. Moreover we show that the solutions are axially symmetric. Furthermore we establish Lipschitz continuity and the decay rate of the solutions.