Using the Hirota bilinear formalism we build the Hirota bilinear form and construct the multisoliton solutions for the coupled semidiscrete additive Bogoyavlensky system with branched dispersion, proving its complete integrability. The same result can be reached also applying the periodic reduction technique. Starting from a general completely integrable “diagonal” equation in two dimensions and performing periodic reduction, one can obtain coupled completely integrable equations. The idea is to consider that the independent discrete variable of the analysed equation is in fact diagonal in a two-dimensional lattice. Imposing periodic reduction on one such coordinate in the 2D-lattice, one can obtain coupled integrable systems with branched disperssion. We will exemplify the technique on the semidiscrete additive Bogoyavlensky equation (aB), which is an
integrable semidiscrete generalized Volterra type equation.