This article is cited in 1 paper

Integrable symplectic maps via reduction of Bäcklund transformation

Dianlou Du, Yuanyuan Lui, Xue Wang

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China

Abstract: We discuss the stationary potential equations as illustrative examples to explain how to construct integrable symplectic maps via Bäcklund transformations. We first give a terse survey of Bäcklund transformations of the potential KdV equation and the potential fifth-order KdV equation. Then, using Jacobi–Ostrogradsky coordinates, we obtain canonical Hamiltonian forms of the stationary potential equations. Finally, we construct symplectic maps from the reduction of a Bäcklund transformation and verify that they are integrable.

Keywords: integrable symplectic map, stationary potential KdV equation, Bäcklund transformation, Lax representation.

Received: 07.12.2020
Revised: 20.01.2021

DOI: 10.4213/tmf10023

 English version: Theoretical and Mathematical Physics, 2021, 208:1, 886–895

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