We obtain the Lie symmetries of two (2+1)-dimensional differential-difference equations based on the extended Harrison and Estabrook's geometric approach that is extended from the continuous differential equations to the differential-difference equations. Moreover, it is shown that both of the two equations possess a Kac–Moody–Virasoro symmetry algebra.
Based on the extended Harrison and Estabrook's differential form method, we obtain the Lie symmetries of two (2+1)-dimensional Toda-like lattices from two different sets of differential forms, respectively. Moreover it is shown that, for each lattice, the determining equations for the two sets give the same symmetries; and the set of differential forms for the lower-dimensional space can make the computation for finding symmetries simpler than the other.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.