New applications of the singular manifold method to the (2 + 1)-dimensional Burgers equations

New applications of the singular manifold method are presented to a (2 + 1)-dimensional Burgers equation and a higher-order Burgers equation. By choosing different seed solutions, auto-Bäcklund transformations, Cole–Hopf transformations and general functional separation solutions containing three arbitrary functions are obtained for the equations in question. Localized coherent structures are for the first time expressed by Jacobi elliptic functions (not infinite periodic limit). And their interaction properties are numerically studied.