Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations

DOI10.1111/SAPM.12346zbMATH Open1476.37080arXiv2001.05423OpenAlexW3102084191MaRDI QIDQ4995576

Meng-Meng Jiang, Xiaoxue Xu, F. W. Nijhoff

Publication date: 25 June 2021

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Abstract: In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg-de Vries-type (KdV-type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.

Full work available at URL: https://arxiv.org/abs/2001.05423

zbMATH Keywords

integrable Hamiltonian systems Baker-Akhiezer functions integrable symplectic maps finite genus solutions discrete Korteweg-de Vries-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) Partial difference equations (39A14) Symplectic and canonical mappings (37J11) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70)

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