Differential substitutions for non-Abelian equations of KdV type

TL;DR

This paper develops non-Abelian analogs of KdV-type equations, including exponential Calogero--Degasperis and Schwarzian KdV equations, with arbitrary parameters, expanding the understanding of non-Abelian integrable systems.

Contribution

It introduces new non-Abelian versions of classical KdV equations and their differential substitutions, incorporating arbitrary non-Abelian parameters.

Findings

Constructed non-Abelian analogs of KdV equations.

Developed differential substitutions with non-Abelian parameters.

Extended classical equations to non-Abelian frameworks.

Abstract

We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of the Schwarzian KdV equation. Equations and differential substitutions under study contain arbitrary non-Abelian parameters.