New symmetry reduction method for (1+1)-dimensional differential-difference equations

Abstract

We propose a new symmetry reduction method for (1+1)-dimensional differential-difference equations (DDEs), namely, the λ-symmetry reduction method of solving ordinary differential equations is generalized to DDEs. Order-reduction processes are a consequence of the invariance of the given DDE under vector fields of the new class. These vector fields satisfy a new prolongation formula. A simple example of order-reduction is provided to illustrate the application.