Deautonomisation of differential-difference equations and discrete Painlevé equations (Q1573912)

Integrable differential-difference equations are studied and their non-autonomous extensions are obtained by using discrete/continuous integrability criterion. Nonautonomous forms of the higher modified KdV equations are considered from the integrability point of view. It is shown that the systematic implementation of the singularity confinement discrete integrability criterion, makes it possible to derive the integrable forms. It is demonstrated to derive discrete equations by combining members of the KdV family with the higher flows of the same hierarchy and then perform the stationary reduction.