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On the algebra of nonlocal symmetries for the 4D Martínez Alonso–Shabat equation
Journal of Geometry and Physics ( IF 1.5 ) Pub Date : 2021-01-16 , DOI: 10.1016/j.geomphys.2021.104122
I.S. Krasil’shchik , P. Vojčák

We consider the 4D Martínez Alonso–Shabat equation E uty=uzuxyuyuxz (also referred to as the universal hierarchy equation) and using its known Lax pair construct two infinite-dimensional differential coverings over E. In these coverings, we give a complete description of the Lie algebras of nonlocal symmetries. In particular, our results generalize the ones obtained in Morozov and Sergyeyev (2014) and contain the constructed there infinite hierarchy of commuting symmetries as a subalgebra in a much bigger Lie algebra.



中文翻译:

关于4DMartínezAlonso–Shabat方程的非局部对称性的代数

我们考虑4DMartínezAlonso–Shabat方程 Ë üŤÿ=üžüXÿ-üÿüXž (也称为通用层次方程),并使用其已知的Lax对构造两个无穷维覆盖 Ë。在这些覆盖物中,我们对非局部对称性的李代数给出了完整的描述。尤其是,我们的结果概括了在Morozov和Sergyeyev(2014)中获得的结果,并在其中包含了更大的李代数中作为子代数构造的无限的交换对称层次。

更新日期:2021-01-20
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