Lax representation is an important characteristic for a given integrable system since one could derive many if not all properties of the equation are determined from its Lax operator. Unfortunately, there is no systematic way to find a Lax representation for a given differential equation. However, there is an alternative, namely starting from a general Lax operator and then doing proper reductions. This approach emerged in the late seventies of last century and turns to be fruitful. One of the authors (Mikhailov) showed that some interesting systems appear from reductions.
The present paper contains the latest result of Mikhailov and his collaborators. Here, the Lax operator takes values in \(sl(N, \mathbb{C})\) and the reduction group is a dihedral group. Interestingly, some new integrable equations are found.