We study the relation between Galois group G of a linear difference-differential system and two classes C1 C2 groups that are specializations difference equation differential in this respectively. show almost all C1∪C2 algebraic subgroups G, there is nonempty subset such product any pair from these subsets. These results have potential application to computation system. also give criterion for ...

Abstract We propose a new method to tackle the integrability problem for evolutionary differential–difference equations of arbitrary order. It enables us produce necessary conditions, determine whether given equation is integrable or not, and advance in classification equations. define develop symbolic representation difference polynomial ring, operators formal series. In order formulate we int...