Higher symmetries of the lattices in 3D

It is known that there is a duality between the Davey–Stewartson type coupled systems and a class of integrable two–dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the lattices can be interpreted as dressing chains for the systems. In our recent study we have found a novel lattice which apparently is not related to the known ones by Miura type transformation. In the article we described higher symmetries to this lattice and derived a new coupled system of the DS type.