Coupled Multicomponent First Multiplicative Bogoyavlensky Lattice and Its Multisoliton Solutions

This study addresses the complete integrability of a generalized multicomponent version of the first multiplicative Bogoyavlensky lattice with branched dispersion. The analysis is performed using the Hirota bilinear formalism and the periodic reduction technique. Initially, a two-dimensional mB1 lattice is considered, for which complete integrability is established by constructing its bilinear form and general multisoliton solutions via the Hirota bilinear formalism. A periodic reduction along the discrete independent variable is then applied to derive the coupled multicomponent mB1 lattice, along with its corresponding bilinear representation and multisoliton solutions. The resulting system serves as an integrable semi-discrete generalization of the classical Volterra-type equation. These findings contribute to the broader understanding of integrable lattice systems with branched dispersion relations and provide a constructive framework for obtaining explicit soliton solutions in multicomponent systems, which exhibit rich internal symmetry structures.