This article studies the discrete Zakharov equations with impulsive effect. The authors first prove that the problem is global well-posed and that the process formed by the solution operators possesses a pullback attractor. Then they establish that there is a family of invariant Borel probability measures contained in the pullback attractor, and that this family of measures satisfies the Liouville type theorem piecewise and is a statistical solution of the impulsive discrete Zakharov equations.

In this paper, the authors investigate the probability distribution of solutions within the time-dependent phase spaces for the lattice Zakharov equations with varying coefficients via the pullback attractors and the notion of generalized Banach limits. They firstly show that the addressed initial value problem is globally well-posed and prove that the related evolution process has a time-dependent pullback attractor on the time-dependent phase spaces. Then they construct a family of invariant Borel probability measures with supports contained in the pullback attractor. Furthermore, they prove that the constructed family of invariant measures is a statistical solution for the addressed lattice Zakharov equations and that Liouville's theorem holds true.