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.
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Funding
The paper is supported by the EPSRC grant EP/P012698/1. JPW would like to thank the EPSRC for funding this research. This work was done during the visit of XJD and CZL in the University of Kent, which is supported by the China Scholarship Council. XJD and CZL would like to thank the School of Mathematics, Statistics & Actuarial Science of Kent University for the hospitality. CZL is supported by the National Natural Science Foundation of China under Grant No. 12071237 and K. C. Wong Magna Fund in Ningbo University.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 347-360 https://doi.org/10.4213/tmf10031.
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Duan, X., Li, C. & Wang, J.P. Multi-component Toda lattice in centro-affine \({\mathbb R}^n\). Theor Math Phys 207, 701–712 (2021). https://doi.org/10.1134/S0040577921060027
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DOI: https://doi.org/10.1134/S0040577921060027