AUTHOR=Lyu Jielin , Shi Kaizhong , Ren Bo , Jin Yongyang 

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

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1237805

DOI=10.3389/fphy.2023.1237805

ISSN=2296-424X

ABSTRACT=<p>We propose a new symmetry reduction method for (1+1)-dimensional differential-difference equations (DDEs), namely, the <italic>λ</italic>-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.</p>