Abstract
We investigate two topics of the constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations. For the constrained dKP hierarchy, the constraint on the Lax operator \({(L^k)_{<0}=q\Delta^{-1}r}\) is shown to be equivalent to a constraint on the tau function, which provides another description of the constrained dKP hierarchy. We also find that there are two different choices of the generating functions in gauge transformation operators of the constrained discrete KP hierarchy.
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The work is supported by National Natural Science Foundation of China under grant Nos. 11505046 and 12171472.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 214, pp. 387–409 https://doi.org/10.4213/tmf10352.
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Song, JQ., Li, C., Cheng, JP. et al. Constrained discrete KP hierarchy: The constraint on the tau functions and gauge transformations. Theor Math Phys 214, 334–353 (2023). https://doi.org/10.1134/S0040577923030030
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DOI: https://doi.org/10.1134/S0040577923030030