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arXiv · 2506.01932

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

Diego Catalano Ferraioli·Tarcísio Castro Silva
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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.

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Diego Catalano Ferraioli, Tarcísio Castro Silva. 2025-06-02. Nonlocal pseudosymmetries and B\"acklund transformations as $\mathcal{C}$-morphisms. https://doi.org/10.1016/j.jde.2026.114334

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