2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215084Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.18 pages, 4 figuresExactly Solvable and Integrable Systemstext