Abstract
We recently constructed a series of integrable discrete autonomous equations on a quadratic lattice with a nonstandard structure of higher symmetries. Here, we construct a modified series using discrete nonpoint transformations. We use both noninvertible linearizable transformations and nonpoint transformations that are invertible on the solutions of the discrete equation. As a result, we obtain several new examples of discrete equations together with their higher symmetries and master symmetries. The constructed higher symmetries give new integrable examples of five- and seven-point differential–difference equations together with their master symmetries. The method for constructing noninvertible linearizable transformations using conservation laws is considered for the first time in the case of discrete equations.
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Notes
Without going into the details, we note that there is a connection between these master symmetries, i.e., the example obtained from (27) is not essentially new.
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Funding
The research of R. N. Garifullin was done in the framework of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District (Supplementary Agreement No. 075-02-2020-1421/1 to Agreement No. 075-02-2020-1421).
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Garifullin, R.N., Yamilov, R.I. Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure. Theor Math Phys 205, 1264–1278 (2020). https://doi.org/10.1134/S0040577920100025
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DOI: https://doi.org/10.1134/S0040577920100025