Integral preserving discretization of 2D Toda lattices

Abstract There are different methods of discretizing integrable systems. We consider semi-discrete analog two-dimensional Toda lattices associated to the Cartan matrices simple Lie algebras that was proposed by Habibullin in 2011. This discretization is based on notion Darboux integrability. Generalized known be continuous case (that is, they admit complete families characteristic integrals both directions). prove analogs all integrable. By examining properties Habibullin’s we show if a function integral for generalized lattice case, then same as well. such integral-preserving discretizations existence second direction.