On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation

Jirina Jahnova; Petr Vojcak

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arXiv · 2310.11194

On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation

Jirina Jahnova·Petr Vojcak

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Abstract

We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang-Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector-functions of the nonlocal symmetries simply by matrix multiplication. We investigate their algebraic properties and discuss the $\mathbb{R}$-algebra structure on the set of all recursion operators for full-fledged nonlocal symmetries of the equation in question. Finally, we illustrate the actions of the obtained recursion operators on particularly chosen full-fledged symmetries and emphasize their advantages compared to the actions of traditionally used recursion operators for shadows.

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BibTeX RIS

Jirina Jahnova, Petr Vojcak. 2023-10-17. On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation. https://arxiv.org/abs/2310.11194

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