Nonlocal pseudosymmetries and B\"acklund transformations as $\mathcal{C}$-morphisms

TL;DR

This paper presents a novel approach to deriving Bäcklund transformations as nonlocal -morphisms using factorisation with respect to nonlocal pseudosymmetries, supported by illustrative examples.

Contribution

It introduces a new method to obtain Bäcklund transformations via nonlocal pseudosymmetries and -morphisms, with a focus on invariants and factorisation techniques.

Findings

Bäcklund transformations can be derived from nonlocal pseudosymmetries.

The approach is demonstrated through several illustrative examples.

Basic invariants determine the Bäcklund transformations.

Abstract

In this paper, we show how factorisation with respect to nonlocal pseudosymmetries allows one to obtain B\"acklund transformations, interpreted as nonlocal $\mathcal{C}$-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.