Abstract
We investigate the integrability of a family of pentagram maps proposed by M. Glick and P. Pylyavskyy, which share the property that each generates an infinite configuration of points and lines with four points on each line. Their Lax representations with spectral parameters are constructed. It’s important to emphasize that the proofs we provide are presented at a physical level of rigor, acknowledging that the periodicity aspect requires further meticulous treatment to establish complete mathematical rigor. Moreover, our investigation reveals a connection between these pentagram-type maps and the discrete KP equation. Finally, their continuous limits are considered.
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The author was supported by the National Natural Science Foundation of China (Nos. 12201325, 12235007). The authors would like to thank the anonymous referee for valuable comments.
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Wang, B. Pentagram-Type Maps and the Discrete KP Equation. J Nonlinear Sci 33, 101 (2023). https://doi.org/10.1007/s00332-023-09961-7
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DOI: https://doi.org/10.1007/s00332-023-09961-7