Nonlocal pseudosymmetries and B\"acklund transformations as $\mathcal{C}$-morphisms
Differential Geometry
2026-04-17 v6 Mathematical Physics
math.MP
Abstract
In this paper, we show how factorisation with respect to nonlocal pseudosymmetries allows one to obtain B\"acklund transformations, interpreted as nonlocal -morphisms of differential equations. According to this approach, which is illustrated through several examples, the B\"acklund transformations are determined by basic invariants of the exploited nonlocal pseudosymmetries.
Cite
@article{arxiv.2506.01932,
title = {Nonlocal pseudosymmetries and B\"acklund transformations as $\mathcal{C}$-morphisms},
author = {Diego Catalano Ferraioli and Tarcísio Castro Silva},
journal= {arXiv preprint arXiv:2506.01932},
year = {2026}
}
Comments
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