![Sample our Computer Science journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5928/TOC-Subject-Sample-2021-Computer-Science.jpg"})
Abstract
Systems of discrete equations on a quadrilateral graph related to the series 
of the affine Lie algebras are studied. The systems are derived from the Hirota-Miwa equation by imposing boundary conditions compatible with the integrability property. The Lax pairs for the systems are presented. It is shown that in the continuum limit the quad systems tend to the corresponding systems of the differential equations belonging to the wellknow Drinfeld-Sokolov hierarchies. The problem of finding the formal asymptotic expansion of the solutions to the Lax equations is studied. Generating functions for the local conservation laws are found for the system corresponding to 
. An example of the higher symmetry is presented.