Continuous symmetries of the lattice potential KdV equation

Levi, Decio; Petrera, Matteo

doi:10.1088/1751-8113/40/15/006

Cited by 33 publications

(52 citation statements)

References 25 publications

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“…We refer to the papers [3,24,28,17,18,27] for some recents results about these equations. Our main purpose is the analysis of their transformation properties.…”

Section: Introductionmentioning

confidence: 99%

On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations

Levi

Petrera

Scimiterna

et al. 2008

SIGMA

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Abstract. We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund transformations for some particular cases of the discrete Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis. All of them generate Bäcklund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability.

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“…We refer to the papers [3,24,28,17,18,27] for some recents results about these equations. Our main purpose is the analysis of their transformation properties.…”

Section: Introductionmentioning

confidence: 99%

On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations

Levi

Petrera

Scimiterna

et al. 2008

SIGMA

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“…As was showed in [12] for the case of the lattice potential KdV equation, there is no combination of eq. (18) with isospectral symmetries which gives us a symmetry of eq.…”

Section: Generalized Symmetries Of the Lskdv Equationmentioning

confidence: 95%

“…A different class of symmetries can be obtained applying the following theorem, introduced in [12], which provides a constructive tool to obtain generalized symmetries for the lSKdV equation (2). Theorem 1.…”

Section: Generalized Symmetries Of the Lskdv Equationmentioning

confidence: 99%

The lattice Schwarzian KdV equation and its symmetries

Levi¹,

Petrera²,

Scimiterna³

2007

J. Phys. A: Math. Theor.

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Abstract. In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.

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“…The aim of this section is to fix the notation and to introduce the formulae necessary to reduce lattice equations in the framework of the discrete reductive perturbation technique [6,8].…”

Section: The Discrete Perturbation Techniquementioning

confidence: 99%

“…Recently this approach has been extended to the case of equations living on lattices [6,8]. Here we apply it to the case of a discrete-time lattice sine-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%