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.

中文翻译：

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通过减少 Bäcklund 变换的可积辛映射

摘要

我们讨论平稳势方程作为说明性示例，以解释如何通过 Bäcklund 变换构造可积辛映射。我们首先简要介绍势KdV方程和势五阶KdV方程的Bäcklund变换。然后，使用 Jacobi-Ostrogradsky 坐标，我们获得了平稳势方程的典型哈密顿形式。最后，我们从 Bäcklund 变换的约简构造辛映射并验证它们是可积的。