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- W2950573216 abstract "We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers $M$. All the equations have a first integral of the first order in one of directions of the two-dimensional lattice. The minimal order of a first integral in the other direction is equal to $3M$ for an equation with the number $M$. In the cases $M=1, 2, 3$ we show that those equations are integrable in quadratures. More precisely, we construct their general solutions in terms of the discrete integrals. We also construct a modified series of Darboux integrable discrete equations which have in different directions the first integrals of the orders $2$ and $3M-1$, where $M$ is the equation number in series. Both first integrals are unobvious in this case." @default.
- W2950573216 created "2019-06-27" @default.
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- W2950573216 date "2019-06-11" @default.
- W2950573216 modified "2023-09-23" @default.
- W2950573216 title "On a series of Darboux integrable discrete equations on the square lattice" @default.
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- W2950573216 doi "https://doi.org/10.48550/arxiv.1906.04503" @default.
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