We consider the problem of propagation of large-intensity monochromatic radiation in a solid with the three-dimensional superlattice of quantum dots interlinked by strong tunneling along one axis. Electrons are treated in a classical way in the formalism of the Boltzmann kinetic equation for the distribution function. Analysis of the Maxwell equations for this case yields a (2+1)-dimensional equation, which has a form similar to the Schrödinger nonlinear equation. Various regimes of the electromagnetic-field propagation were numerically analyzed. The super-Gaussian light beam was found to undergo a waist stage, and the interaction of light beams led to their merging.