关于4D Martínez Alonso-Shabat方程的非局部对称代数
On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation
摘要：
考虑四维Mart 'ınez Alonso-Shabat方程$u_{ty} = u_z u_{xy} - u_y u_{xz}$（也称为泛族方程），利用其已知的拉克斯对构造了$\mathcal{E}$上的两个无穷维微分覆盖.在这些覆盖中，我们给出了非局部对称李代数的完整描述。特别地，我们的结果推广了[O.I.Morozov，A.Sergyeyev，The four-dimensional Mart\'ınez Alonso-shabat equation：reductions and nonlocal symmetries. J. of Geom. and Phys. 85（2014），40- 45（arXiv：1401.7942v2）]，并包含在那里构造的交换对称的无限层次作为一个更大的李代数中的子代数。
英文摘要：
We consider the 4D Mart\'ınez 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\'ınez 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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