Complete list of Darboux Integrable Chains of the form $t_{1x}=t_x+d(t,t_1)$

Ismagil Habibullin, Natalya Zheltukhina, Asli Pekcan

We study differential-difference equation of the form $$\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$$ with unknown $t(n,x)$ depending on continuous and discrete va…