Geodesic
Modified series of integrable discrete equations on a~quadratic lattice with a~nonstandard symmetry structure
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 23-40

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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.
Keywords: discrete equation, higher symmetry, master symmetry, differential–difference equation
Mots-clés : noninvertible transformation. 
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     author = {R. N. Garifullin and R. I. Yamilov},
     title = {Modified series of integrable discrete equations on a~quadratic lattice with a~nonstandard symmetry structure},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--40},
     publisher = {mathdoc},
     volume = {205},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a1/}
}
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R. N. Garifullin; R. I. Yamilov. Modified series of integrable discrete equations on a~quadratic lattice with a~nonstandard symmetry structure. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 23-40. http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a1/