Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

We study the Veronese web equation uyutx+λuxuty−(λ+1)utuxy=0 and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Final...

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Bibliographic Details
Published in:Journal of geometry and physics 2019-12, Vol.146, p.103519, Article 103519
Main Authors: Krasil’shchik, I.S., Morozov, O.I., Vojčák, P.
Format: Article
Language:English
Subjects:
Differential coverings
Lax pairs
Master symmetries
Nonlocal symmetries
Recursion operators
Veronese web equation
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Summary:We study the Veronese web equation uyutx+λuxuty−(λ+1)utuxy=0 and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Finally, we construct a recursion operator and explore its action on nonlocal shadows. The operator provides a new shadow which serves as a master-symmetry.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2019.103519