ORIGINAL PAPER
On the Einstein–Weyl geometrical system with the central quadric ansatz: The associated dispersionless integrable hierarchy
Yuxiao Du,
Kelei Tian,
Ying Xu,
Ge Yi,
Yuxiao Du
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorKelei Tian
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorYing Xu
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorCorresponding Author
Ge Yi
School of Mathematics, Hefei University of Technology, Hefei, China
Correspondence
Ge Yi, School of Mathematics, Hefei University of Technology, Hefei 230601, China.
Email: [email protected]
Search for more papers by this authorYuxiao Du,
Kelei Tian,
Ying Xu,
Ge Yi,
Yuxiao Du
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorKelei Tian
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorYing Xu
School of Mathematics, Hefei University of Technology, Hefei, China
Search for more papers by this authorCorresponding Author
Ge Yi
School of Mathematics, Hefei University of Technology, Hefei, China
Correspondence
Ge Yi, School of Mathematics, Hefei University of Technology, Hefei 230601, China.
Email: [email protected]
Search for more papers by this authorFirst published: 19 May 2025
Abstract
In this paper, we focus on a typical integrable dispersionless equation, which corresponds to an Einstein–Weyl geometrical equation with the central quadric ansatz. It can be considered as a (2+1)-dimensional dispersionless integrable system arising from the commutation condition of the Lax pair of a one-parameter family of vector fields. The associated dispersionless integrable hierarchy with infinite symmetries is defined, and the Lax–Sato equations are obtained. Meanwhile, two types of reductions of the hierarchy are shown.
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