An Unusual Series of Autonomous Discrete Integrable Equations on a Square Lattice

Garifullin, R. N.; Yamilov, R. I.

doi:10.1134/s0040577919070031

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…In this paper we limited ourselves to present the result of the algebraic entropy test for equation (51b), which suggests integrability. More details and generalizations, including L − A pairs, on equation (51b) can be found in [19].…”

Section: Discussionmentioning

confidence: 99%

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Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Garifullin¹,

Gubbiotti²,

Yamilov³

2021

JNMP

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In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.

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Section: Discussionmentioning

confidence: 99%

“…It can be proved that equation (51b) does not admit any autonomous generalized symmetries of lower order. Equation (51b) seems to be a new interesting example and deserves a separate study, see [19].…”

Section: And the Trivial Linearizable Equation (8a)mentioning

confidence: 99%

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Garifullin¹,

Gubbiotti²,

Yamilov³

2021

JNMP

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“…An analogous series of the continuous hyperbolic type equations is discussed in [14]. In [7] a series of the sine-Gordon type autonomous discrete equations is presented. Autonomous generalized symmetries and conservation laws in both directions may have arbitrarily high minimal orders in this case.…”

Section: Introductionmentioning

confidence: 99%

On series of Darboux integrable discrete equations on square lattice

Garifullin

Yamilov

2019

Ufimsk. Mat. Zh.

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We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers . 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 3 for an equation with the number .In the cases = 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 3 −1, where is the equation number in series. Both first integrals are unobvious in this case.

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Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure

Garifullin

Yamilov

2020

Theor Math Phys

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An Unusual Series of Autonomous Discrete Integrable Equations on a Square Lattice

Cited by 6 publications

References 23 publications

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

On series of Darboux integrable discrete equations on square lattice

Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure

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