2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185780We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky's (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra $\sl_2^{tor}$.10 pages, 4 figures, pLaTeX2e, uses amsmath, amssymb, amsthm, graphicxExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryMathematical PhysicsQuantum AlgebraRepresentation Theorytext