2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80520We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the $CP^1$ topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schrödinger hierarchy.23 pages, a remark at the end of Section 4 addedExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryDifferential Geometrytext