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arXiv · 2008.10281

On the algebra of nonlocal symmetries for the 4D Mart\'{\i}nez Alonso-Shabat equation

I. S. Krasil'shchik·P. Vojcak
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Abstract

We consider the 4D Mart\'{\i}nez Alonso-Shabat equation $u_{ty} = u_z u_{xy} - u_y u_{xz}$ (also referred to as the universal hierarchy equation) and using its known Lax pair construct two infinite-dimensional differential coverings over $\mathcal{E}$. In these coverings, we give a complete description of the Lie algebras of nonlocal symmetries. In particular, our results generalize the ones obtained in [O.I.Morozov, A.Sergyeyev, The four-dimensional Mart\'{\i}nez Alonso-shabat equation: reductions and nonlocal symmetries. J. of Geom. and Phys. 85 (2014), 40--45 (arXiv:1401.7942v2)] and contain the constructed there infinite hierarchy of commuting symmetries as a subalgebra in a much bigger Lie algebra.

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I. S. Krasil'shchik, P. Vojcak. 2020-08-24. On the algebra of nonlocal symmetries for the 4D Mart\'{\i}nez Alonso-Shabat equation. https://arxiv.org/abs/2008.10281

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