Nonlocal pseudosymmetries and Bäcklund transformations as $\mathcal{C}$-morphisms

Abstract

In this paper, we show how factorisation with respect to nonlocal pseudosymmetries allows one to obtain Bäcklund transformations, interpreted as nonlocal $\mathcal{C}$-morphisms of differential equations. According to this approach, which is illustrated through several examples, the Bäcklund transformations are determined by basic invariants of the exploited nonlocal pseudosymmetries.

Published Open Access in J. Differential Equations. This version replaces the previous preprint and includes all final corrections. Please cite and access the official version at https://doi.org/10.1016/j.jde.2026.114334

References in corpus (2)

• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• On the Geometry of Twisted Symmetries: Gauging and Coverings