The nonlinear equation is obtained describing the dynamics of nonlinear wave structures in the dusty plasma above the illuminated surface of the Moon in the case of low frequencies and pancake-like shape of wave packet in the direction along the external magnetic field. This equation is the modified Zakharov-Kuznetsov equation. The analytical formula for the one-dimensional soliton solution is derived. The analysis of the stability of one-dimensional soliton solution was performed.