Xiaojuan Duan, Chuanzhong Li, Jing Ping Wang, “Multi-component Toda lattice in centro-affine <nobr>${\mathbb R}^n$</nobr>”, TMF, 2021, Volume 207, Number 3,Pages <nobr>347

Multi-component Toda lattice in centro-affine ${\mathbb R}^n$

Xiaojuan Duan^a, Chuanzhong Li^bc, Jing Ping Wang^d

^a Department of Mathematics and Physics, Xiamen University of Technology, Xiamen, China
^b School of Mathematics and Statistics, Ningbo University, Ningbo, China
^c College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China
^d School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UK

Abstract: We use the group-based discrete moving frame method to study invariant evolutions in a $n$-dimensional centro-affine space. We derive the induced integrable equations for invariants, which can be transformed to local and nonlocal multi-component Toda lattices under a Miura transformation, and thus establish their geometric realizations in centro-affine space.

Keywords: discrete moving frame, multi-component Toda lattices, Hamiltonian structures.

MSC: 37K10, 37K60

Received: 13.12.2020
Revised: 13.12.2020

DOI: 10.4213/tmf10031