On the hierarchies of the fully nonlinear Möbius-invariant and symmetry-integrable evolution equations of order three

Abstract

This is a follow-up paper to the results published in Studies in Applied Mathematics143, 139–156 (2019), where we reported a classification of 3rd- and 5th-order semi-linear symmetry-integrable evolution equations that are invariant under the Möbius transformation, which includes a list of fully nonlinear 3rd-order equations that admit these properties. In the current paper we propose a simple method to compute the higher-order equations in the hierarchies for the fully nonlinear 3rd-order equations. We apply the proposed method to compute the 5th-order members of the hierarchies explicitly.