2023/10/17 by Jiřina Jahnová, Jahnova, Jirina, P. Vojčák +1
Mathematics · Physics and Astronomy · #35B06 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2310.11194
openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.