Lax integrable nonlinear partial difference equations

New Integrable and Linearizable Nonlinear Difference Equations

“…Recently we considered Lax matrices with rational entries, having the form P Q where both P and Q are linear in v l m , v l+1 m and v l m+1 and reported several new nonlinear PΔΔE's satisfying (2.3) and hence they are integrable in the sense of Lax [30]. In this article we wish to consider Lax matrices again with rational entries in which P and Q are algebraic polynomials of degree greater than one and show that there exists a class of nonlinear PΔΔE's satisfying the compatibility condition (2.3).…”