Reductions and conserved quantities for discrete compound KdV-Burgers equations

We present two methods to reduce the discrete compound KdV-Burgers equation,which are reductions of the independent and dependent variables:the translational invariant method has been applied in order to reduce the independent variables;and a discrete spectral matrix has been introduced to reduce the number of dependent variables.Based on the invariance of a discrete compound KdV-Burgers equation under infinitesimal transformation with respect to its dependent and independent variables,we present the determining equations of transformation Lie groups for the KdV-Burgers equation and use the characteristic equations to obtain new forms of invariants.