Generalized symmetry integrability test for discrete equations on the square lattice

DOI10.1088/1751-8113/44/14/145207zbMath1225.37079arXiv1011.0070OpenAlexW2102913856MaRDI QIDQ2994814

Ravil I. Yamilov, Decio Levi

Publication date: 29 April 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0070

zbMATH Keywords

conservation lawsdifference equationsLax pairVolterra-type equationsKlein-type equationsMiura-type equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Symmetries and conservation laws in mechanics of particles and systems (70S10) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Partial difference equations (39A14)

Related Items (17)

On the inverse problem of the discrete calculus of variations ⋮ Classification of variational multiplicative fourth-order difference equations ⋮ Non-existence of S-integrable three-point partial difference equations in the lattice plane ⋮ The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation ⋮ Classification of five-point differential–difference equations II ⋮ Reconstructing a lattice equation: a non-autonomous approach to the Hietarinta equation ⋮ Classification of five-point differential-difference equations ⋮ Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure ⋮ Darboux transformations and recursion operators for differential-difference equations ⋮ Second order integrability conditions for difference equations: an integrable equation ⋮ Discrete equation on a square lattice with a nonstandard structure of generalized symmetries ⋮ Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations ⋮ An unusual series of autonomous discrete integrable equations on a square lattice ⋮ Determining the symmetries of difference equations ⋮ Algebraic entropy of a class of five-point differential-difference equations ⋮ Features of Discrete Integrability ⋮ Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations ^*

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