On the Classification of Darboux Integrable Chains

Ismagil Habibullin, Natalya Zheltukhina, Aslı Pekcan

We study differential-difference equation of the form $t_x(n+1)=f(t(n),t(n+1),t_x(n))$ with unknown $t=t(n,x)$ depending on $x$, $n$. The equation is called Darboux integrable, i…