PreHamiltonian and Hamiltonian operators for differential-difference equations

DOI10.1088/1361-6544/ab5912zbMath1436.37076arXiv1808.02957OpenAlexW3002468006MaRDI QIDQ5212119

Jing Ping Wang, Sylvain Carpentier, Alexander V. Mikhailov

Publication date: 27 January 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02957

zbMATH Keywords

integrable systemsdifference equationsbi-Hamiltonian structureHamiltonian operatorsdifference algebrapseudo-difference operatorspre-Hamiltonian operators

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Difference operators (39A70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06) Integrable difference and lattice equations; integrability tests (39A36)

Related Items (5)

Generalized conditional symmetries and pre-Hamiltonian operators ⋮ Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions ⋮ A Darboux-Getzler theorem for scalar difference Hamiltonian operators ⋮ Multi-component Toda lattice in centro-affine \(\mathbb{R}^n\) ⋮ Rational recursion operators for integrable differential-difference equations

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